Non-volatile (nv) memory (nvm) matrix circuits employing nvm matrix circuits for performing matrix computations

ABSTRACT

Non-volatile (NV) memory (NVM) matrix circuits employing NVM circuits for performing matrix computations are disclosed. In exemplary aspects disclosed herein, an NVM matrix circuit is provided that has a plurality of NVM storage string circuits each comprising a plurality of NVM bit cell circuits each configured to store a memory state. Each NVM bit cell circuit has a stored memory state represented by a resistance, and includes a transistor whose gate node is coupled to a word line among a plurality of word lines configured to receive an input vector of 1×m size for example. Activation of the gate of a given NVM bit cell circuit controls whether its resistance is contributed to a respective source line. This causes a summation current to be generated on each source line based on the weighted summed contribution of each NVM bit cell circuit&#39;s resistance to its respective source line.

PRIORITY APPLICATION

The present application claims priority under 35 U.S.C. § 119(e) to U.S. Provisional Patent Application Ser. No. 62/531,921 entitled “MATRIX CIRCUITS EMPLOYING NON-VOLATILE (NV) MEMORY CIRCUITS FOR PERFORMING MATRIX COMPUTATIONS” and filed on Jul. 13, 2017, which is incorporated herein by reference in its entirety.

RELATED APPLICATIONS

The present application is related to U.S. Provisional Patent Application Ser. No. 62/531,924 entitled “MULTI-LEVEL CELL (MLC) MATRIX CIRCUITS EMPLOYING NON-VOLATILE (NV) MLC MEMORY CIRCUITS FOR PERFORMING MATRIX COMPUTATIONS” and filed on Jul. 13, 2017, which is incorporated herein by reference in its entirety.

The present application is also related to U.S. patent application Ser. No. ______, entitled “MULTIPLE (MULTI-) LEVEL CELL (MLC) NON-VOLATILE (NV) MEMORY (NVM) MATRIX CIRCUITS FOR PERFORMING MATRIX COMPUTATIONS WITH MULTI-BIT INPUT VECTORS” and filed on Nov. 20, 2017, which is incorporated herein by reference in its entirety.

BACKGROUND I. Field of the Disclosure

The technology of the disclosure relates generally to computerization of biological networks, and more particularly to circuit network implementations of synapse networks to provide matrix multiplication with artificial intelligence (AI) learning.

II. Background

Biological networks are networks that apply to biological systems. For example, the biological circulatory system in a human involves the function of pumping and channeling of blood through blood vessels to the body, the lungs, and the heart. Network representation of intracellular biological networks typically considers molecular components within a cell as nodes and their direct or indirect interactions as links. The recognition of biological networks has motivated the development of various neuromorphic computing systems whose architectures reflect the general organizational principles of nervous systems in an effort to partially reproduce the immense efficiency advantage that biological computation exhibits in some problems. These neuromorphic systems are organized as populations of excitatory and inhibitory spiking neurons (i.e., nerve cells that are specialized cells transmitting nerve impulses) with configurable synaptic connections. Synaptic plasticity plays a crucial role in allowing neural networks to learn and adapt to various input environments. Thus, neuromorphic systems implemented in computer networks need to implement plastic synapses in circuits to obtain basic “cognitive” capabilities such as learning.

Synapses outnumber neurons by several orders of magnitude in biological neural networks. Reproducing these biological features in neuromorphic electronic circuits presents a scaling problem, as integrating thousands of dedicated synapse circuits per neuron can quickly become infeasible for circuit systems that require a large number of neurons. This scaling problem in computer networks has traditionally been solved by either treating synapses as simple linear elements and time-multiplexing spikes from many pre-synaptic sources onto the same linear circuit, or by treating them as basic binary elements that can be set either on or off externally, without learning abilities. Real synapses, however, exhibit non-linear phenomena like spike timing dependent plasticity (STDP) that modulate the weight of an individual synapse based on the activity of the pre- and post-synaptic neurons. The modulation of synaptic weights through plasticity has been shown to greatly increase the range of computations that neural networks can perform.

Capturing the plasticity properties of real synapses in analog neuromorphic hardware requires the use of distinct physical circuits/elements for each synapse. In conventional complementary metal oxide semiconductor (CMOS) circuit technology, this can lead to restrictions on scalability. Some potential solutions to the scalability issues in pure CMOS technology involve the use of very large integrated structures or the adoption of deep submicron technologies. For example, microchip CMOS circuit implementations of STDP rules may result in about thirty (30) transistors per plastic synapse, and thus may lead to high costs for their hardware realization. There is, overall, general thinking that STDP is very expensive to implement in conventional CMOS microchips. Scalability restrictions however can be greatly relaxed if one resorts to compact nano-scale circuit elements that can reproduce the plasticity properties of real synapses. One potential candidate for these elements is a memristor. A memristor is an element which behaves somewhat like a non-linear resistor with memory. In the neuromorphic community, memristors are seen as ideal devices for synapse implementations, as they combine three (3) key functions in one device. Memristors are non-linear, passive, two-terminal electrical devices that relate to electrical charge and magnetic flux linkage. A memristor's electrical resistance is not constant, but depends on the history of current that had previously flowed through the device. That is, its present resistance depends on how much electric charge has flowed in what direction through it in the past. Thus, a memristor device remembers its history, which is called its non-volatility property. When the electric power supply is turned off to the memristor, the memristor remembers its most recent resistance until it is turned on again. Memristors can implement biologically realistic synaptic weight updates (i.e., learning), can carry out long-term multi-valued weight storage, and can also communicate weighted pre-synaptic activity to the postsynaptic side, significantly relaxing scalability restrictions.

STDP can be implemented with just one (1) memristor per synapse if appropriate peripheral signal conditioning neurons are used in hybrid CMOS/memristor realizations. Typically, plasticity in these memristor synapses is evoked by applying specific waveforms to the two (2) terminals of the memristor, with the waveforms aligned to pre-respectively postsynaptic pulses. The correlation of the waveforms across the memristor in turn implements STDP-like plasticity with the form of the STDP curve defined by the applied wave shape. Both hardware and software models of plasticity based on the basic STDP mechanism are typically chosen, primarily for their simplicity.

In this regard, FIG. 1A illustrates a matrix network circuit 100 as a cross-bar network that includes a way of interconnecting memristors and CMOS circuit neurons for STDP learning. The matrix network circuit 100 includes a first resistive random access memory (RRAM) cross-bar network 102A and a second RRAM cross-bar network 102B. Each of the first and second RRAM cross-bar networks 102A, 102B include respective memristors 104A, 104B at respective synaptic junctions 106A, 106B each representing individual synapses. CMOS buffer gates 108A, 108B, 108C represent three (3) layers of neurons, referred to as CMOS circuit neurons 108A, 108B, 108C. FIG. 1B illustrates a synaptic connection for a post-synaptic CMOS circuit neuron 108 formed by controlling the first and second RRAM cross-bar networks 102A, 102B. The flat side of the CMOS circuit neuron 108 is its input node 110 (i.e., dendrites) and the sharp side of the CMOS circuit neuron 108 is its output node 112 (i.e., axon). The CMOS circuit neuron 108 controls a voltage V_(post) at its input node 110 and a voltage V_(pre) at its output node 112. When the CMOS circuit neuron 108 is not spiking, it forces a constant voltage at both input and output nodes 110, 112, while collecting through its input node 110 the sum of input synaptic spike currents I₁, I₂ coming from the memristors 104A, 104B, which contribute to changing the neuron internal state. When the CMOS circuit neuron 108 spikes, it sets a one-spike waveform at both input and output nodes 110, 112. In this manner, the CMOS circuit neuron 108 sends its output spikes forward as pre-synaptic spikes for the destination synaptic memristors, but also backward to preceding synaptic memristors as post-synaptic spikes.

Neural networks that employ memristor networks for providing synapses can also be used for other applications that require weighted matrix multiplication computations, such as convolution for example. For example, FIG. 2A illustrates a memristor cross-bar synapse matrix 200 with a pre-neuron layer 202 of pre-neuron circuits 204(1)-204(m) and a post-neuron layer 206 of post-neuron circuits 208(1)-208(n). Synapses can be provided between the pre-neuron circuits 204(1)-204(m) and the post-neuron circuits 208(1)-208(m). It may be desired to sum up the multiplication of the state of each pre-neuron circuit 204(1)-204(m) with the state of each post-neuron circuit 208(1)-208(n) to provide an accelerated weighted sum and weight update. For example, FIG. 2B illustrates a memristor cross-bar matrix circuit 212 of the memristor cross-bar synapse matrix 200 in FIG. 2A. The memristor cross-bar matrix circuit 212 includes an RRAM cross-bar array circuit 214 with rows R₁-R_(m) and columns C₁-C_(n) of memristors 216(1)(1)-216(m)(n) that can form respective synapses 210(1)(1)-210(m)(n). The memristors 216(1)(1)-216(m)(n) are configured to store a memory state of an m×n matrix. Input voltages V₁₋V_(m) may be for a 1×m input vector. It may be desired to multiply an input vector by the m×n matrix provided by the memristors 216(1)(1)-216(m)(n). The memristors 216(1)(1)-216(m)(n) in each column C₁-C_(n) of are coupled to each other in parallel. Thus, the conductance of the RRAM cross-bar array circuit 214 represents the weight of the memristor cross-bar matrix circuit 212. The individual sums of the currents I₁-I_(n) represent the weight (i.e., the conductance) of the selected column C₁-C_(n) of memristors 2160(1)-216( )(n) multiplied by the state of the pre-neuron circuits 204(1)-204(m) represented by the input voltages V₁₋V_(m). For example, current I₁ is the sum of each input voltage V₁₋V_(m) from a pre-neuron circuit 204(1)-204(m) in a selected row R₁-R_(m) multiplied by the conductance of a respective memristor 216(1)(1)-216(m)(1) when column C₁ is selected, according to the formula:

$I_{j} = {\sum\limits_{i}\; {G_{ij} \cdot V_{i}}}$

-   -   where:         -   i=rows R₁-R_(m); and         -   j=columns C₁-C_(n).

Thus, current I₁ is the sum of the conductance of memristor 216(1)(1) times input voltage V₁, plus the conductance of memristor 216(1)(2) times input voltage V₂, . . . , plus the conductance of memristor 216(1)(m) times input voltage V_(m). The weight of the memristor cross-bar matrix circuit 212 (i.e., the conductances of each memristor 216(1)(1)-216(m)(n)) is updated to provide training based on output voltages of each of the post-neuron circuits 208(1)-208(n) applied backward to preceding input voltages V₁-V_(m) of the pre-neuron circuits 204(1)-204(m).

The memristor cross-bar matrix circuit 212 in FIG. 2B has a sneak path current issue. Sneak path current is current that flows from an addressed row R₁-R_(m) to and adjacent row R₁-R_(m). For example, assume that column C₁ in the cross-bar synapse weight matrix circuit 214 is selected. A current flows in column C₁ not only through selected memristors 216(1)(1)-216(m)(1) in column C₁ to post-neuron circuit 208(1), but a sneak current also flows back into pre-neuron circuit 204(1). It may not be possible to distinguish the sneak-current leading to an incorrect updating of the weight of the memristor cross-bar matrix circuit 212. Further, RRAM technologies, such as memristors, may not have highly repeatable resistances leading to retention issues that can cause incorrect calculations. Endurance of RRAM technologies may also be limited.

SUMMARY OF THE DISCLOSURE

Aspects disclosed in the detailed description include non-volatile (NV) memory (NVM) matrix circuits employing NVM matrix circuits for performing matrix computations. In exemplary aspects disclosed herein, an NVM matrix circuit is provided that has a plurality of NVM storage string circuits each comprising a plurality of NVM bit cell circuits organized in respective memory rows and each configured to store a memory state. For example, the NVM matrix circuit may form an m×n NVM matrix circuit, where ‘m’ represents the number of memory rows of NVM storage string circuits provided, and ‘n’ represents the number of NVM bit cell circuits within each NVM storage string circuit provided in respective memory columns. A plurality of bit lines are provided and each configured to be coupled to a respective NVM storage string circuit. A plurality of source lines are provided and each configured to be coupled to a respective NVM storage string circuit. Each NVM bit cell circuit has a stored memory state represented by a resistance, and includes a transistor whose gate node is coupled to a word line among a plurality of word lines configured to receive an input vector of 1×m size for example. Activation of the gate of a given NVM bit cell circuit controls whether its resistance is contributed to a respective source line. For example, the input vector could be a pre-synapse weight vector for example. Each source line is coupled to a respective output node wherein the source lines for all the NVM storage string circuits can collectively provide an output vector. The output vector may be a post-synapse vector for example. To multiply an input vector of 1×m size times the m×n memory matrix circuit formed by the plurality of NVM storage string circuits, a line voltage is applied to the bit lines of the NVM storage string circuits while input voltages representing an input vector are applied to gate nodes of the NVM bit cell circuits of the NVM storage string circuits. This causes a summation current to be generated on each source line based on the weighted summed contribution of each NVM bit cell circuit's resistance to its respective source line. Each output line forms an output vector, which is the result of the 1×m input vector times one (1) column n of the m×n NVM matrix circuit. By the NVM bit cell circuits of the NVM storage string circuits including a transistor coupled to a word line that controls the resistance presented on its respective source line, a cross-bar connection between the word lines and the bit lines does not have to be provided which avoids creating sneak path currents in the NVM matrix circuit. The word lines and the bit lines are isolated from each other through the NVM bit cell circuits.

In this regard, in one aspect, an NVM matrix circuit is provided. The NVM matrix circuit comprises a plurality of word lines configured to receive an input vector represented by an input voltage on each word line among the plurality of word lines. The NVM matrix circuit also comprises a plurality of bit lines and a plurality of source lines. Each bit line among the plurality of bit lines is configured to receive a corresponding line voltage. The NVM matrix circuit further comprises a plurality of NVM storage string circuits, each configured to be electrically coupled between a corresponding bit line among the plurality of bit lines and a corresponding source line among the plurality of source lines each comprising a plurality of NVM bit cell circuits. Each NVM bit cell circuit among the plurality of NVM bit cell circuits has a resistance representing a stored memory state in the NVM bit cell circuit to form a data vector for the corresponding NVM storage string circuit. Each NVM bit cell circuit among the plurality of NVM bit cell circuits in the NVM storage string circuit comprises a gate node coupled to a corresponding word line among the plurality of word lines. Each NVM bit cell circuit is configured to couple its resistance to the source line in response to the input voltage applied to the corresponding word line coupled to the gate node. The NVM matrix circuit further comprises a plurality of access transistors. Each access transistor is coupled to a corresponding bit line among the plurality of bit lines and a corresponding NVM storage string circuit among the plurality of NVM storage string circuits coupled to the source line corresponding to the bit line. Each access transistor comprises an access gate node coupled to an access line, and is configured to electrically couple the corresponding bit line to the corresponding NVM storage string circuit in the response to an access voltage applied to the access gate node.

In another aspect, an NVM matrix circuit is provided. The NVM matrix circuit comprises a plurality of means for applying a plurality of input voltages representing an input vector, a plurality of means for applying a plurality of line voltages, and a plurality of means for providing a plurality of output currents representing an output vector. The NVM matrix circuit further comprises a plurality of NVM storage string means each electrically coupled to a corresponding means for applying an input voltage among the plurality of means for applying the plurality of input voltages and a corresponding means for providing an output current among the plurality of means for providing the plurality of output currents. Each of the plurality of NVM storage string means comprises a plurality of NV means for storing a memory state, each having a resistance representing the stored memory state to form a data vector for a corresponding NVM storage string means among the plurality of NVM storage string means. Each plurality of NV means for storing the memory state comprises a means for electrically coupled the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents. Each NV means also comprises a means for controlling coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents. The NVM matrix circuit further comprises a plurality of access means for controlling the means for electrically coupling the corresponding means for applying the input voltage among the plurality of means for applying the plurality of input voltages to a corresponding NVM storage string means in the coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents.

In a further aspect, a method of performing matrix multiplication in an NVM matrix circuit is provided. The method comprises applying a line voltage on at least one bit line among a plurality of bit lines coupled to a corresponding NVM storage string circuit among a plurality of NVM storage string circuits, to electrically couple the line voltage to the corresponding NVM storage string circuit coupled to a corresponding bit line among the plurality of bit lines. Each NVM storage string circuit comprises a plurality of NVM bit cell circuits each having a resistance representing a stored memory state in the NVM bit cell circuit to form a data vector for the corresponding NVM storage string circuit. The method further comprises applying a second line voltage on at least one source line among a plurality of source lines coupled to a corresponding NVM storage string circuit among the plurality of NVM storage string circuits, to electrically coupled the second line voltage to the corresponding NVM storage string circuit coupled to a corresponding source line among the plurality of source lines. The method further comprises applying a plurality of input voltages representing an input vector on a plurality of word lines, wherein each word line is coupled to a corresponding gate node of an NVM bit cell circuit in each of the plurality of NVM storage string circuits, to electrically couple the NVM bit cell circuit to the source line to couple the resistance of the NVM bit cell circuit to the source line. The method further comprises applying an access voltage to a plurality of access transistors, wherein each access transistor is coupled to a corresponding bit line among the plurality of bit lines and a corresponding NVM storage string circuit among the plurality of NVM storage string circuits coupled to the source line corresponding to the bit line, to electrically couple the corresponding bit line to the corresponding NVM storage string circuit.

In another aspect, an NVM matrix system is provided that comprises a first NVM matrix circuit and a second NVM matrix circuit. The first NVM matrix circuit comprises a plurality of first word lines configured to receive a first input vector represented by a first input voltage on each first word line among the plurality of first word lines. The first NVM matrix circuit further comprises a plurality of first bit lines, and a plurality of first source lines. Each first bit line among the plurality of first bit lines is configured to receive a corresponding first line voltage. Each first source line is coupled to a first output node among a plurality of first output nodes. The first NVM matrix circuit also comprises a plurality of first NVM storage string circuits, each configured to be electrically coupled between a corresponding first bit line among the plurality of first bit lines and a corresponding first source line among the plurality of first source lines. Each first NVM storage string circuit comprises a plurality of first NVM bit cell circuits. Each first NVM bit cell circuit among the plurality of first NVM bit cell circuits has a resistance representing a stored memory state in the first NVM bit cell circuit to form a first data vector for the corresponding first NVM storage string circuit. Each first NVM bit cell circuit comprises a first gate node coupled to a corresponding first word line among the plurality of first word lines, and is configured to couple its resistance to the first source line in response to the first input voltage applied to the corresponding first word line coupled to the first gate node. The second NVM matrix circuit comprises a plurality of second word lines each coupled to an output node among the plurality of first output nodes. The second NVM matrix circuit further comprises a plurality of second bit lines, and a plurality of second source lines. Each second bit line among the plurality of second bit lines is configured to receive a corresponding second line voltage. Each second source line is coupled to a second output node among a plurality of second output nodes. The second NVM matrix circuit also comprises a plurality of second NVM storage string circuits, each configured to be electrically coupled between a corresponding second bit line among the plurality of second bit lines and a corresponding second source line among the plurality of second source lines. Each second NVM storage string circuit comprises a plurality of second NVM bit cell circuits. Each second NVM bit cell circuit among the plurality of second NVM bit cell circuits has a resistance representing a stored memory state in the second NVM bit cell circuit to form a second data vector for the corresponding second NVM storage string circuit. Each second NVM bit cell circuit comprises a second gate node coupled to a corresponding second word line among the plurality of second word lines, and is configured to couple its resistance to the second source line in response to a second input voltage applied to the corresponding second word line coupled to the second gate node.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A is an exemplary matrix network circuit employing memristor networks to provide synapses for complementary metal oxide semiconductor (CMOS) circuit neurons;

FIG. 1B illustrates an exemplary synaptic connection for a post-synaptic CMOS circuit neuron in the matrix network circuit of FIG. 1A;

FIG. 2A illustrates an exemplary memristor cross-bar matrix circuit;

FIG. 2B illustrates an exemplary memristor cross-bar matrix circuit employing an RRAM cross-bar array circuit;

FIG. 3A is a schematic diagram of an exemplary non-volatile (NV) memory (NVM) matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NAND NVM flash circuits and each comprised of a plurality of NVM flash bit cell circuits for performing matrix computations;

FIG. 3B is a schematic diagram of an exemplary two-dimensional (2D) NAND NVM flash circuit that can be an NVM bit cell circuit in the NVM matrix circuit in FIG. 3A;

FIG. 4A illustrates an exemplary logic ‘0’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 4B illustrates an exemplary logic ‘1’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 5 illustrates an exemplary read operation in the NVM matrix circuit in FIG. 3A;

FIG. 6A illustrates another exemplary logic ‘0’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 6B illustrates another exemplary logic ‘1’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 7A illustrates another exemplary logic ‘0’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 7B illustrates another exemplary logic ‘1’ write operation in the NVM matrix circuit in FIG. 3A;

FIG. 8A is a flowchart illustrating an exemplary process of performing a write operation in the NVM matrix circuit in FIG. 3A;

FIG. 8B is a flowchart illustrating an exemplary process of performing a read operation in the NVM matrix circuit in FIG. 3A;

FIG. 9 is an example of the NVM matrix system that includes the NVM matrix circuit in FIG. 3A and another NVM matrix circuit like the NVM matrix circuit in FIG. 3A being configured and/or reconfigured and coupled to the first NVM matrix circuit to provide neuron layers for a synapse NVM matrix circuit;

FIG. 10 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NAND NVM ferroelectric (Fe) Field-Effect Transistor (FET) (FeFET) circuits each comprising a plurality of NVM FeFET bit cell circuits for performing matrix computations;

FIG. 11 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of AND NVM flash circuits each comprised of a plurality of NVM flash bit cell circuits for performing matrix computations;

FIG. 12 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of AND NVM FeFET circuits each comprised of a plurality of NVM FeFET bit cell circuits for performing matrix computations;

FIG. 13 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of AND NVM magneto-resistive random access memory (MRAM) circuits each comprised of a plurality of NVM MRAM bit cell circuits for performing matrix computations;

FIG. 14 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of AND NVM resistive random access memory (RRAM) circuits each comprised of a plurality of NVM RRAM bit cell circuits for performing matrix computations;

FIG. 15 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NOR NVM flash circuits each comprised of a plurality of NVM flash bit cell circuits for performing matrix computations;

FIG. 16 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NOR NVM FeFET circuits each comprised of a plurality of NVM FeFET bit cell circuits for performing matrix computations;

FIG. 17 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NOR NVM MRAM circuits each comprised of a plurality of NVM MRAM bit cell circuits for performing matrix computations;

FIG. 18 is a schematic diagram of an exemplary NVM matrix circuit without need for cross-bar connections employing NVM storage string circuits in the form of NOR NVM RRAM circuits each comprised of a plurality of NVM RRAM bit cell circuits for performing matrix computations;

FIG. 19 is a block diagram of an exemplary chip package that includes a system-on-a-chip (SoC), a dedicated memory chip, and a dedicated NVM matrix circuit chip that can include NVM matrix circuits disclosed herein, including without limitation the NVM matrix circuits in FIGS. 3A-18; and

FIG. 20 is a block diagram of an exemplary processor-based system that includes memory systems that can include NVM matrix circuits disclosed herein, including without limitation the NVM matrix circuits in FIGS. 3A-18.

DETAILED DESCRIPTION

With reference now to the drawing figures, several exemplary aspects of the present disclosure are described. The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any aspect described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects.

Aspects disclosed in the detailed description include non-volatile (NV) memory (NVM) matrix circuits employing NVM matrix circuits for performing matrix computations. In exemplary aspects disclosed herein, an NVM matrix circuit is provided that has a plurality of NVM storage string circuits each comprising a plurality of NVM bit cell circuits organized in respective memory rows and each configured to store a memory state. For example, the NVM matrix circuit may form an m×n NVM matrix circuit, where ‘m’ represents the number of memory rows of NVM storage string circuits provided, and ‘n’ represents the number of NVM bit cell circuits within each NVM storage string circuit provided in respective memory columns. A plurality of bit lines are provided and each configured to be coupled to a respective NVM storage string circuit. A plurality of source lines are provided and each configured to be coupled to a respective NVM storage string circuit. Each NVM bit cell circuit has a stored memory state represented by a resistance, and includes a transistor whose gate node is coupled to a word line among a plurality of word lines configured to receive an input vector of 1×m size for example. Activation of the gate of a given NVM bit cell circuit controls whether its resistance is contributed to a respective source line. For example, the input vector could be a pre-synapse weight vector for example. Each source line is coupled to a respective output node wherein the source lines for all the NVM storage string circuits can collectively provide an output vector. The output vector may be a post-synapse vector for example. To multiply an input vector of 1×m size times the m×n memory matrix circuit formed by the plurality of NVM storage string circuits, a line voltage is applied to the bit lines of the NVM storage string circuits while input voltages representing an input vector are applied to gate nodes of the NVM bit cell circuits of the NVM storage string circuits. This causes a summation current to be generated on each source line based on the weighted summed contribution of each NVM bit cell's resistance to its respective source line. Each output line forms an output vector, which is the result of the 1×m input vector times one (1) column n of the m×n NVM matrix circuit. By the NVM bit cell circuits of the NVM storage string circuits including a transistor coupled to a word line that controls the resistance presented on its respective source line, a cross-bar connection between the word lines and the bit lines does not have to be provided which avoids creating sneak path currents in the NVM matrix circuit. The word lines and the bit lines are isolated from each other through the NVM bit cell circuits.

In this regard, FIG. 3A is a schematic diagram of an exemplary NVM matrix circuit 300 that can perform matrix multiplication without the use of cross-bar connections. The NVM matrix circuit 300 employs NVM storage string circuits 302(0)-302(m) in ‘m+1’ memory rows R₀-R_(m) that each include a plurality of NVM bit cell circuits R₀₀-R_(mn) in FIG. 3A. In this example, the NVM storage string circuits 302(0)-302(m) are NAND NVM flash circuits wherein the NVM bit cell circuits R₀₀-R_(mn) are NVM flash circuits. However, the NVM storage string circuits 302(0)-302(m) can be provided as other types of NVM matrix circuits as discussed in more detail below in other aspects. The NVM bit cell circuits R₀₀-R_(mn) in each respective NVM storage string circuit 302(0)-302(m) are arranged in memory rows R₀-R_(m) and memory columns C₀-C_(n). The NVM matrix circuit 300 includes a respective bit line BL₀-BL_(m) for each memory row R₀-R_(m). Bit line driver circuits 306(0)-306(m) are provided that are each configured to drive a respective line voltage V₀-V_(m) on the respective bit lines BL₀-BL_(m). Source lines SL₀-SL_(m) are also provided that are each coupled to a respective output node 308(0)-308(m). The NVM storage string circuits 302(0)-302(m) are coupled between a corresponding bit line BL₀-BL_(m) and a corresponding source line SL₀-SL_(m) in each respective memory row R₀-R_(m). The source lines SL₀-SL_(m) are configured to carry a respective current I₀-I_(m) to the respective output nodes 308(0)-308(m) as an output vector S₀-S_(m) when their respective NVM bit cell circuits R₀₀-R_(mn) are activated. For example, the output vector S₀-S_(m) may be a binary post-synapse vector.

With continuing reference to FIG. 3A, the NVM matrix circuit 300 also includes a respective word line WL₀-WL_(n) for each memory column C₀-C_(n). Word line driver circuits 310(0)-310(n) are provided that are each configured to drive a respective input vector X₀-X_(n) comprising a plurality of input voltages on the respective word lines WL₀-WL_(n). As will be discussed in more detail below, the word lines WL₀-WL_(n) are coupled to respective gate nodes G₀₀-G_(mn) of the NVM bit cell circuits R₀₀-R_(mn) in a given memory column C₀-C_(n) to control the resistances of the NVM bit cell circuits R₀₀-R_(mn) being applied to the respective source lines SL₀-SL_(m). For example, the input vector X₀-X_(n) may be a binary pre-synapse data vector. The NVM matrix circuit 300 also includes first access transistors 312(0)-312(m) coupled between a respective bit line BL₀-BL_(m) and an NVM storage string circuit 302(0)-302(m). The first access transistors 312(0)-312(m) each comprise a first access gate node G coupled to a respective first access line 314 configured to be driven with a first access voltage by a first access line driver circuit 316. The first access transistors 312(0)-312(m) are each configured to control whether a corresponding line voltage V₀-V_(m) applied on a respective bit line BL₀-BL_(m) is applied to a respective NVM storage string circuit 302(0)-302(m) in a corresponding memory row R₀-R_(m). The first access transistors 312(0)-312(m) are configured to pass a line voltage V₀-V_(m) on respective bit lines BL₀-BL_(m) in response to a first access signal (voltage) driven by the first access line driver circuit 316 onto a second access line 320 to the first access gate node G of the first access transistors 312(0)-312(m) sufficient to turn on the first access transistors 312(0)-312(m). The NVM matrix circuit 300 also includes second access transistors 318(0)-318(m) coupled between a respective NVM storage string circuit 302(0)-302(m) and a source line SL₀-SL_(m) coupled to the output nodes 308(0)-308(m). The second access transistors 318(0)-318(m) are each configured to couple a respective NVM storage string circuit 302(0)-302(m) to a respective source line SL₀-SL_(m) and a respective output node 308(0)-308(m) in response to a second access signal (voltage) driven by the second access line driver circuit 322 onto the second access line 320 to a second access gate node G of the second access transistors 318(0)-318(m) sufficient to turn on the second access transistors 318(0)-318(m). As shown in FIG. 3A, there is no cross-bar coupling between the word lines WL₀-WL_(n) and the bit lines BL₀-BL_(m). The access transistors 312(0)-312(m), 318(0)-318(m) of the NVM storage string circuits 302(0)-302(m) can provide further isolation between the word lines WL₀-WL_(n) and the bit lines BL₀-BL_(m).

With continuing reference to FIG. 3A, each NVM bit cell circuit R₀₀-R_(mn) in the NVM matrix circuit 300 is an NVM flash circuit that does not need power to retain data in this example. FIG. 3B is a schematic diagram of an exemplary two-dimensional (2D) NAND flash memory circuit that can be provided as the NVM storage string circuits 302(0)-302(m) in the NVM matrix circuit 300 in FIG. 3A. FIG. 3B illustrates an exemplary NVM storage string circuit 302(0) that can be provided in memory row R₀ in the NVM matrix circuit 300 in FIG. 3A as an example in both a circuit and layout diagram. As shown in FIG. 3B, the NVM bit cell circuits R₀₀-R_(mn) are each coupled to each other in a series-coupled, string fashion, which source nodes S₀₀-S_(0n-1) of the NVM bit cell circuits R₀₀-R_(n-1) are coupled to drain nodes D₀₁-D_(0n) of an adjacent NVM bit cell circuit R₀₁-R_(0n). The end NVM bit cell circuits R₀₀, R_(n) in the NVM storage string circuit 302(0) are coupled to respective access transistors 312(0), 318(0). Each NVM bit cell circuit R₀₀-R_(0n) has a resistance representing a stored memory state. Each NVM bit cell circuit R₀₀-R_(mn) has a transistor comprising a gate G₀₀-G_(0n) that is coupled to a respective word line WL₀-WL_(n) based on in which memory column C₀-C_(n) the NVM bit cell circuit R₀₀-R_(mn) is located. Each NVM bit cell circuit R₀₀-R_(mn) is configured to be activated to activate a semiconductor channel to couple its resistance on a respective source line SL₀-SL_(m) in its memory row R₀-R_(m). The collective memory states in the NVM bit cell circuits R₀₀-R_(0n) form a data vector stored in the NVM storage string circuit 302(0). As shown in FIG. 3B, there is no cross-bar coupling between the word line WL₀ and the bit line BL₀, which is also true between all word lines WL₀-WL_(n) and the respective bit lines BL₀-BL_(m).

With continuing reference to FIG. 3B, as will be discussed in more detail below, when a line voltage in applied to bit line BL₀ and access voltages are applied to the access gate nodes G of the access transistors 312(0)-312(m) sufficient to activate the semiconductor channels C of the access transistors 312(0)-312(m), the NVM storage string circuit 302(0) is coupled to the bit line BL₀ and the source line SL₀. The input voltages as an input vector X₀-X_(n) applied to the word lines WL₀-WL_(n) and gate nodes G₀₀-G_(0n) of the respective NVM bit cell circuits R₀₀-R_(0n) as an input vector X₀-X_(n) control activation of the respective NVM bit cell circuits R₀₀-R_(0n). When activated, the NVM bit cell circuits R₀₀-R_(0n) couple their resistances to the source line SL₀. The resistances of the NVM bit cell circuits R₀₀-R_(0n) are a function of their stored memory states. Thus, the resistances of the NVM bit cell circuits R₀₀-R_(0n) can represent a weight vector. The current I₀ flowing on a respective source line SL₀ to the output node 308(0) is a function of the sum of the dot product multiplications of the respective input vector X₀-X_(n) multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n) of the NVM storage string circuit 302(0). Thus, with reference to FIG. 3A, all the NVM bit cell circuits R₀₀-R_(0n) for the NVM storage string circuits 302(0)-302(m) in the NVM matrix circuit 300 in FIG. 3A can represent a weight matrix. The current I₀-I_(m) flowing from the respective source lines SL₀-SL_(M) of the respective NVM storage string circuits 302(0)-302(m) to output nodes 308(0)-308(m) is a function of the respective line voltages V₀-V_(m) driven by the bit line driver circuits 306(0)-306(m) on the respective source lines SL₀-SL_(m) divided by the summed channel resistances of the NVM bit cell circuits R₀₀-R_(mn) of the NVM storage string circuits 302(0)-302(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 300 in FIG. 3A is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{i} = {V_{BL}/{\sum\limits_{j}\; R_{ij}}}$

-   -   where:         -   i=memory row 0 to m;         -   j=memory column 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=resistance of an NVM bit cell circuit.

Thus, with continuing reference to FIG. 3A, the NVM matrix circuit 300 is configured to perform matrix multiplication of each of the 1×n weight vectors stored as respective memory states in each of the NVM storage string circuits 302(0)-302(m) by the n×1 input vector X₀-X_(n) simultaneously. The dot products of these vector multiplications are provided as a function of the respective amplitudes of the currents I₀-I_(m) generated at the output nodes 308(0)-308(m) according to the current formula provided above.

Further, if the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 308(0)-308(m) are coupled to a post-neuron layer, the NVM matrix circuit 300 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   R_(ij)=resistance of an NVM bit cell circuit; and         -   S=value at source lines of NVM bit cell circuits.

The weight matrix of the NVM matrix circuit 300 provided as stored memory states in the NVM bit cell circuits R₀₀-R_(mn) can be set to the desired memory states in a write operation to provide the desired weight matrix. For example, FIG. 4A illustrates writing a logic ‘0’ in a write operation to the NVM bit cell circuit R₂₅ in the NVM matrix circuit 300 in FIG. 3A. As shown therein, to write a logic ‘0’ to NVM bit cell circuit R₂₅ in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuit 306(2) on the bit line BL₂ for memory row R₂ depending on whether the NVM bit cell circuit R₂₅ stores a memory state with or without a charge trap, respectively. A line voltage of 5V is applied on source line SL₂ coupled to the output node 308(2). An input voltage of 10V is applied to the word line WL₂ to be applied to the gate node G₂₅ of the NVM bit cell circuit R₂₅ to program the memory state of the NVM bit cell circuit R₂₅ to a logic ‘0’ memory state. Similarly, FIG. 4B illustrates writing a logic ‘1’ in a write operation to the NVM bit cell circuit R₂₅ in the NVM matrix circuit 300 in FIG. 3A. As shown therein, to write a logic ‘1’ to NVM bit cell circuit R₂₅ in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuit 306(2) on the bit line BL₂ for memory row R₂ depending on whether the NVM bit cell circuit R₂₅ stores a memory state without or with a charge trap, respectively. A line voltage of 0V is applied on the source line SL₂ coupled to the output node 308(2). A voltage of −10 V is applied to the word line WL₂ to be applied to the gate node G₂₅ of the NVM bit cell circuit R₂₅ to program the memory state of NVM bit cell circuit R₂₅ to a logic ‘1’ memory state.

FIG. 5 illustrates an exemplary read operation in the NVM matrix circuit 300 in FIG. 3A. A read operation is performed to cause the NVM matrix circuit 300 to perform a matrix computation. To multiply the input vector X₀-X_(n) times the memory states of each of the NVM storage string circuits 302(0)-302(m) to generate respective currents I₀-I_(m) on the source lines SL₀-SL_(m) coupled to the output nodes 308(0)-308(m), all the NVM bit cell circuits R₀₀-R_(mn) are activated in this example. In this regard, in this example, an input voltage of 4.5 V is applied as the input vector X₀-X_(n) to each of the respective word lines WL₀-WL_(n) to cause the channel resistances of each of the NVM bit cell circuits R₀₀-R_(mn) added in series to contribute to the overall series resistance of the respective source lines SL₀-SL_(m). Their channel resistances contribute to the overall series resistance of respective source lines SL₀-SL_(m) and are a function of the memory states stored in the NVM bit cell circuits R₀₀-R_(mn). The currents I₀-I_(m) at the output nodes 308(0)-308(m) are a function of the sum of the dot product multiplications of input vectors X₀-X_(n) multiplied by the respective memory states of the NVM bit cell circuits R₀₀-R_(mn) each in the respective NVM storage string circuits 302(0)-302(m) as weight vectors.

More than one NVM bit cell circuit R₀₀-R_(mn) in a given memory row R₀₋R_(m) in the NVM matrix circuit 300 in FIG. 3A can be written to at a time as part of a write operation. In this regard, FIG. 6A illustrates writing a logic ‘0’ in a write operation to the NVM bit cell circuits R₂₂ and R₂₅ in the NVM matrix circuit 300 in FIG. 3A. As shown in FIG. 6A, to write a logic ‘0’ to NVM bit cell circuits R₂₂ and R₂₅ in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuit 306(2) on the bit line BL₂ for memory row R₂ depending on whether the NVM bit cell circuits R₂₂ and R₂₅ store a memory state with or without a charge trap, respectively. A line voltage of 5 V is applied on the source line SL₂. An input (i.e., program) voltage of 10V is applied to the word lines WL₂ and WL₅ to be applied to both gate nodes G₂₂ and G₂₅ of the NVM bit cell circuits R₂₂ and R₂₅ to program the NVM bit cell circuits R₂₂ and R₂₅ to a logic ‘0’ memory state. A different input voltage not sufficient to program the NVM bit cell circuits R₀₀-R_(m0), R₀₁-R_(m1), R₀₃-R_(m3), R₀₄-R_(m4), R₀₆-R_(mn) in memory columns C₀, C₁, C₃, C₄, and C₆₋C_(n) can be applied to write lines WL₀, WL₁, WL₃, WL₄, and WL₆₋WL_(n) for the write operation. Similarly, FIG. 6B illustrates writing a logic ‘1’ in a write operation to the NVM bit cell circuits R₂₂ and R₂₅ in the NVM matrix circuit 300 in FIG. 3A. As shown in FIG. 6B, to write a logic ‘1’ to NVM bit cell circuits R₂₂ and R₂₅ in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuit 306(2) on the bit line BL₂ for memory row R₂ depending on whether the NVM bit cell circuits R₂₂ and R₂₅ store a memory state without or with a charge trap, respectively. A voltage of 0 V is applied on the source line SL₂. An input (i.e., program) voltage of −10V is applied to the word lines WL₂ and WL₅ to be applied to both gate nodes G₂₂ and G₂₅ of the NVM bit cell circuits R₂₂ and R₂₅ to program the NVM bit cell circuits R₂₂ and R₂₅ to a logic ‘1’ memory state.

More than one NVM bit cell circuits R₀₀-R_(mn) in a given memory column C₀₋C_(n) in the NVM matrix circuit 300 in FIG. 3A can be written to at a time as part of a write operation. In this regard, FIG. 7A illustrates writing a logic ‘0’ in a write operation to both NVM bit cell circuits R₂₅ and R_(m-15) in memory column C₅ in the NVM matrix circuit 300 in FIG. 3A. As shown in FIG. 7A, to write a logic ‘0’ to NVM bit cell circuits R₂₅ and R_(m-15) in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuits 306(2), 306(m−1) on the bit lines BL₂ and BL_(m-1) for memory rows R₂ and R_(m-1) depending on whether the NVM bit cell circuits R₂₅ and R_(m-15) store a memory state with or without a charge trap, respectively. A line voltage of 5 V is applied on the source lines SL₂ and SL_(m-1). An input (i.e., program) voltage of 10V is applied to the word line WL₂ to be applied to gate nodes G₂₅ and G_(m-15) of the NVM bit cell circuits R₂₅ and R_(m-15) to program the NVM bit cell circuits R₂₅ and R_(m-15) to a logic ‘0’ memory state. Similarly, FIG. 7B illustrates writing a logic ‘1’ in a write operation to both NVM bit cell circuits R₂₅ and R_(m-15) in memory column C₅ in the NVM matrix circuit 300 in FIG. 3A. As shown in FIG. 7B, to write a logic ‘1’ to NVM bit cell circuits R₂₅ and R_(m-15) in this example, a 0 V or 5 V line voltage is applied by the bit line driver circuits 306(2), 306(m−1) on the bit lines BL₂ and BL_(m-1) for memory row R₂ depending on whether the NVM bit cell circuits R₂₅ and R_(m-15) store a memory state without or with a charge trap, respectively. A line voltage of 0 V is applied on the source lines SL₂ and SL_(m-1). An input (i.e., program) voltage of −10V is applied to the word line WL₂ to be applied to gates G₂₅ and G_(m-15) of the NVM bit cell circuits R₂₅ and R_(m-15) to program the NVM bit cell circuits R₂₅ and R_(m-15) to a logic ‘1’ memory state.

FIG. 8A is a flowchart illustrating an exemplary process 800 of performing a read operation in the NVM matrix circuit 300 in FIG. 3A. Examples of read operations to the NVM matrix circuit 300 in FIG. 3A were discussed above with regard to FIGS. 6A-7B. In this regard, with reference to FIGS. 3A and 8A, the process 800 includes applying a line voltage on at least one bit line BL₀-BL_(m) among a plurality of bit lines BL₀-BL_(m) coupled to a corresponding NVM storage string circuit 302(0)-302(m) among the plurality of NVM storage string circuits 302(0)-302(m), to electrically couple the line voltage to the corresponding NVM storage string circuit 302(0)-302(m) coupled to a corresponding bit line BL₀-BL_(m) among the plurality of bit lines BL₀-BL_(m)(block 802 in FIG. 8A). Each of the plurality of NVM storage string circuits 302(0)-302(m) comprise a plurality of NVM bit cell circuits R_(x0)-R_(xn) among a plurality of bit lines BL₀-BL_(m) each having a channel resistance representing a stored memory state in the NVM bit cell circuit R_(x0)-R_(xn) to form a data vector for the corresponding NVM storage string circuit 302(0)-302(m). The process 800 also involves applying a second line voltage on at least one source line SL₀-SL_(m) among a plurality of source lines SL₀-SL_(m) coupled to a corresponding NVM storage string circuit 302(0)-302(m) among the plurality of NVM storage string circuits 302(0)-302(m), to electrically couple a second line voltage to the corresponding NVM storage string circuit 302(0)-302(m) coupled to a corresponding source line SL₀-SL_(m) among a plurality of source lines SL₀-SL_(m) (block 804 in FIG. 8A). The process 800 also involves applying a plurality of input voltages representing an input vector X₀-X_(n) on a plurality of word lines WL₀-WL_(n), each word line WL₀-WL_(n) among the plurality of word lines WL₀-WL_(n) coupled to a corresponding gate node G₀₀-G_(mn) of an NVM bit cell circuit R₀₀-R_(mn) in each of the plurality of NVM storage string circuits 302(0)-302(m), to electrically couple the NVM bit cell circuit R₀₀-R_(mn) to the source line SL₀-SL_(m) to couple the channel resistance of the NVM bit cell circuit R₀₀-R_(mn) to the source line SL₀-SL_(m) (block 806 in FIG. 8A). The process 800 also involves applying an access voltage to a plurality of access transistors 312(0)-312(m), each access transistor 312(0)-312(m) among the plurality of access transistors 312(0)-312(m) coupled to a corresponding bit line BL₀-BL_(m) among the plurality of bit lines BL₀-BL_(m) and a corresponding NVM storage string circuit 302(0)-302(m) among the plurality of NVM storage string circuits 302(0)-302(m). The plurality of NVM storage string circuits 302(0)-302(m) are coupled to a respective source line SL₀-SL_(m) corresponding to the bit line BL₀-BL_(m), to electrically couple the corresponding bit line BL₀-BL_(m) to the corresponding NVM storage string circuit 302(0)-302(m) (block 808 in FIG. 8A). FIG. 8B is a flowchart illustrating an exemplary process 810 of performing a read operation in the NVM matrix circuit 300 in FIG. 3A. Examples of write operations to the NVM matrix circuit 300 in FIG. 3A were discussed above with regard to FIGS. 5A and 5B. In this regard, with reference to FIGS. 3A and 8B, the process 810 includes applying a line voltage to a bit line BL₀-BL_(m) among the plurality of bit lines BL₀-BL_(m) coupled to a corresponding NVM storage string circuit 302(0)-302(m) among the plurality of NVM storage string circuits 302(0)-302(m) (block 812 in FIG. 8B). The process 810 also involves applying a second line voltage to a source line SL₀-SL_(m) among the plurality of source lines SL₀-SL_(m) coupled to the corresponding NVM storage string circuit 302(0)-302(m) (block 814 in FIG. 8B). The process 810 also involves applying a write activation voltage to a gate node G₀₀-G_(m), of an NVM bit cell circuit R₀₀-R_(mn) in the corresponding NVM storage string circuit 302(0)-302(m) to write a memory state based on the write activation voltage applied to the gate node G₀₀-G_(mn) of the NVM bit cell circuit R₀₀-R_(mn) (block 816 in FIG. 8B).

The NVM matrix circuit 300 in FIG. 3A can also be employed and reconfigured to provide reconfigured neuron paths to support universal deep learning or artificial intelligence (AI) tasks for different neuron layers and neurons. In this regard, FIG. 9 is an example of an NVM matrix system that includes an NVM matrix circuit 300 in FIG. 3A being configured as an n× m NVM matrix circuit 300 like shown in FIG. 3A. Another NVM matrix circuit 300A is provided that is similar to the NVM matrix circuit 300, but is configured as an m× k NVM matrix circuit. The NVM matrix circuits 300, 300A can be coupled together to form first and second respective neuron layers 900(1), 900(2) with output vectors S₀-S_(m) providing intermediate neurons 902. This allows a dot product output vector S₀-S_(m) as a result of the matrix calculation of n× m NVM matrix circuit 300 to be used as an input vector X₀-X_(m) to the NVM matrix circuit 300A to produce dot produce output vectors S₀-S_(k). Thus, the NVM matrix circuit 300 being coupled to the other NVM matrix circuit 300A is configured to produce currents I₀-I_(k) on a hidden layer according to the following formula:

$I_{l} = {V_{BL}/{\sum\limits_{h}\; R_{hl}}}$

-   -   where:         -   h=memory row 0 to m;         -   l=memory column 0 to k;         -   V_(BL)=voltage of bit lines BL₀′-BL_(m)′; and         -   R_(hl)=channel resistances of an NVM bit cell circuit in the             NVM matrix circuit 300A.

The operation of the matrix calculations and write operations that can be performed in the NVM matrix circuits 300, 300A in FIG. 9 can be as previously described for the NVM matrix circuit 300.

Other types of NVM bit cell circuits can be employed besides NAND NVM flash memory circuits like shown in the NVM matrix circuit 300 in FIG. 3A. For example, FIG. 10 is a schematic diagram of another exemplary NVM matrix circuit 1000 without need for cross-bar connections between bit lines and word lines like not included the NVM matrix circuit 300 in FIG. 3A. However, the NVM matrix circuit 1000 includes NVM storage string circuits 1002(0)-1002(m) in the form of NAND NVM ferroelectric (Fe) Field-Effect Transistor (FET) (FeFET) circuits in this example. The NVM bit cell circuits R₀₀-R_(mn) in each respective NVM storage string circuits 1002(0)-1002(m) are NVM FeFET circuits arranged in memory rows R₀-R_(m) and memory columns C₀-C_(n). The NVM matrix circuit 1000 includes a respective bit line BL₀-BL_(m) for each memory row R₀-R_(m). Bit line driver circuits 1006(0)-1006(m) are provided that are each configured to drive a respective line voltage V₀-V_(m) on the respective bit lines BL₀-BL_(m). Source lines SL₀-SL_(m) are also provided that are each coupled to a respective output node 1008(0)-1008(m). The NVM storage string circuits 1002(0)-1002(m) are coupled between a corresponding bit line BL₀-BL_(m) and a corresponding source lines SL₀-SL_(m) in each respective memory row R₀-R_(m). The source lines SL₀-SL_(m) are configured to carry a respective current I₀-I_(m) to the respective output nodes 1008(0)-1008(m) as an output vector when their respective NVM bit cell circuits R₀₀-R_(mn) are activated. For example, the output vector may be a binary post-synapse vector.

With continuing reference to FIG. 10, the NVM matrix circuit 1000 also includes a respective word line WL₀-WL_(n) for each memory column C₀-C_(n). Word line driver circuits 1010(0)-1010(n) are provided that are each configured to drive a respective input vector X₀-X_(n) comprising a plurality of input voltages on the respective word lines WL₀-WL_(n). For example, the input vector X₀-X_(n) may be a binary pre-synapse data vector. The NVM matrix circuit 1000 also includes first access transistors 1012(0)-1012(m) coupled between a respective bit line BL₀-BL_(m) and an NVM storage string circuit 1002(0)-1002(m). The first access transistors 1012(0)-1012(m) each comprise a first access gate node G coupled to a respective first access line 1014 configured to be driven with a first access voltage by a first access line driver circuit 1016. The first access transistors 1012(0)-1012(m) are each configured to control whether a corresponding line voltage V₀-V_(m) applied on a respective bit line BL₀-BL_(m) is applied to a respective NVM storage string circuit 1002(0)-1002(m) in a corresponding memory row R₀-R_(m). The first access transistors 1012(0)-1012(m) are configured to pass a line voltage V₀-V_(m) on respective bit lines BL₀-BL_(m) in response to a first access signal (voltage) driven by the first access line driver circuit 1016 onto a second access line 1020 to the first access gate node G of the first access transistors 1012(0)-1012(m) sufficient to turn on the first access transistors 1012(0)-1012(m). The NVM matrix circuit 1000 also includes second access transistors 1018(0)-1018(m) coupled between a respective NVM storage string circuit 1002(0)-1002(m) and a source line SL₀-SL_(m) coupled to the output nodes 1008(0)-1008(n). The second access transistors 1018(0)-1018(m) are each configured to couple a respective NVM storage string circuit 1002(0)-1002(m) to a respective source line SL₀-SL_(m) and a respective output node 1008(0)-1008(m) in response to a second access signal (voltage) driven by a second access line driver circuit 1022 onto the second access line 1020 to the second access gate node G of the second access transistors 1018(0)-1018(m) sufficient to turn on the second access transistors 1018(0)-1018(m). As shown in FIG. 10, there is no cross-bar coupling between the word lines WL₀-WL_(n) and the bit lines BL₀-BL_(m). The access transistors 1012(0)-1012(m), 1018(0)-1018(m) of the NVM storage string circuits 1002(0)-1002(m) provide isolation between the word lines WL₀-WL_(n) and the bit lines BL₀-BL_(m).

With continuing reference to FIG. 10, each NVM bit cell circuit R₀₀-R_(mn) in the NVM matrix circuit 1000 is an NVM FeFET circuit that does not need power to retain data in this example. The NVM bit cell circuits R₀₀-R_(mn) in this example are each coupled to each other in a series-coupled, string fashion. Using the NVM storage string circuit 1002(0) in memory row R₀ as an example, source nodes of the NVM bit cell circuits R₀₀-R_(n-1) are coupled to the drain nodes of an adjacent NVM bit cell circuit R₀₁-R_(0n). The end NVM bit cell circuits R₀₀, R_(on) in the NVM storage string circuit 1002(0) are coupled to respective access transistors 1012(0), 1018(0). Each NVM bit cell circuit R₀₀-R_(0n) has a resistance representing a stored memory state. Each NVM bit cell circuit R₀₀-R_(mn) has a transistor comprising a gate G₀₀-G_(0n) that is coupled to a respective word line WL₀-WL_(n) based on in which memory column C₀-C_(n) the NVM bit cell circuit R₀₀-R_(mn) is located. Each NVM bit cell circuit R₀₀-R_(mn) is configured to be activated to activate a semiconductor channel to couple its resistance on a respective source line SL₀-SL_(m) in its memory row R₀-R_(m). The collective memory states in the NVM bit cell circuits R₀₀-R_(0n) form a data vector stored in the NVM storage string circuit 1002(0). As shown in FIG. 10, there is no cross-bar coupling between the word line WL₀ and the bit line BL₀, which is also true between all word lines WL₀-WL_(n) and the respective bit lines BL₀-BL_(m).

With continuing reference to FIG. 10, when a line voltage is applied to bit line BL₀ and access voltages are applied to the access gate nodes G of the access transistors 1012(0)-1012(m) sufficient to activate the semiconductor channels C of the access transistors 1012(0)-1012(m), the NVM storage string circuit 1002(0) is coupled to the bit line BL₀ and the source line SL₀. The input voltages as an input vector X₀-X_(n) applied to the word lines WL₀-WL_(n) and the gate nodes G₀₀-G_(0n) as an input vector X₀-X_(n) control activation of the respective NVM bit cell circuits R₀₀-R_(0n). When activated, the NVM bit cell circuits R₀₀-R_(0n) couple their resistances to the source line SL₀. The resistances of the NVM bit cell circuits R₀₀-R_(0n) are a function of their stored memory states. Thus, the resistances of the NVM bit cell circuits R₀₀-R_(0n) can represent a weight vector. The current I₀ flowing on a respective source line SL₀ to the output node 1008(0) is a function of the sum of the dot product multiplications of the respective input vector X₀-X_(n) multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n) of the NVM storage string circuit 1002(0). Thus, with reference to FIG. 10, all the NVM bit cell circuits R₀₀-R_(0n) for the NVM storage string circuits 1002(0)-1002(m) in the NVM matrix circuit 1000 in FIG. 10 can represent a weight matrix. The current I₀-I_(m) flowing from the respective source lines SL₀-SL_(m) of the respective NVM storage string circuits 1002(0)-1002(m) to output nodes 1008(0)-1008(m) is a function of the respective line voltages V₀-V_(m) driven by the bit line driver circuits 1006(0)-1006(m) on the respective source lines SL₀-SL_(m) divided by the summed channel resistances of the NVM bit cell circuits R₀₀-R_(mn) of the NVM storage string circuits 1002(0)-1002(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1000 in FIG. 10 is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{i} = {V_{BL}/{\sum\limits_{j}\; R_{ij}}}$

-   -   where:         -   i=memory row 0 to m;         -   j=memory column 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=channel resistance of an NVM bit cell circuit.

Thus, with continuing reference to FIG. 10, the NVM matrix circuit 1000 is configured to perform matrix multiplication of each of the 1×n weight vectors stored as respective memory states in each of the NVM storage string circuits 1002(0)-1002(m) by the n×1 input vector X₀-X_(n) simultaneously. The summed dot product multiplications of these vector multiplications are provided as a function of the respective amplitudes of the currents I₀-I_(m) generated at the output nodes 1008(0)-1008(m) according to the current formula provided above.

Further, if the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 1008(0)-1008(m) are coupled to a post-neuron layer, the NVM matrix circuit 1000 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   R_(ij)=channel resistance of an NVM bit cell circuit; and         -   S=value at source lines of NVM bit cell circuits.

The weight matrix of the NVM matrix circuit 1000 provided as stored memory states in the NVM bit cell circuits R₀₀-R_(mn) can be set to the desired memory states in a write operation to provide the desired weight matrix. The write and read operations previously described for the NVM matrix circuit 300 in FIG. 3A can be applied to the NVM matrix circuit 1000 in FIG. 10.

FIG. 11 illustrates an NVM matrix circuit 1100 that is a reconfiguration of the NVM matrix circuit 300 in FIG. 3A into an n×m matrix by switching the memory rows and columns to have memory rows R₀₋R_(n) and memory columns C₀₋C_(m). The NVM matrix circuit 1100 includes NVM storage string circuits 1102(0)-1102(m) in the form of AND NVM flash circuits in this example, which are provided in respective memory columns C₀₋C_(m) to provide NVM bit cell circuits R₀₀₋R_(nm). Thus, each NVM bit cell circuit R₀₀₋R_(nm) is an NVM flash circuit. The word lines WL₀₋WL_(n) and bit lines BL₀₋BL_(m) are reversed between memory rows R₀₋R_(n) and columns C₀₋C_(m) from the NVM matrix circuit 300 in FIG. 3A, but are still coupled to the NVM bit cell circuits R₀₀₋R_(nm) in the same manner as in the NVM matrix circuit 300 in FIG. 3A. In this regard, as shown in FIG. 11, word lines WL₀₋WL_(n) that receive input vector X₀-X_(n) in the form of input voltages are provided for each memory row R₀₋R_(n). The bit lines BL₀₋BL_(m) are provided for each memory column C₀₋C_(m). Common components between the NVM matrix circuit 300 in FIG. 3A and the NVM matrix circuit 1100 in FIG. 11 are shown with common element numbers and thus will not be re-described. Read and write operations similar to that described above with regard to the NVM matrix circuit 300 can be performed in the NVM matrix circuit 1100 in FIG. 11.

Each NVM bit cell circuit R₀₀₋R_(nm) has a channel resistance representing a stored memory state. The channel resistances of the NVM bit cell circuits R₀₀-R_(nm) represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(nm) has a transistor comprising a gate node G₀₀-G_(nm) that is coupled to a respective word line WL₀-WL_(n) based on in which memory row R₀-R_(n) the NVM bit cell circuit R₀₀-R_(nm) is located. Each NVM bit cell circuit R₀₀-R_(nm) is configured to activate its semiconductor channel to couple its channel resistance (i.e., conductance) between the respective bit lines BL₀-BL_(m) the respective source line SL₀-SL_(m) in parallel with other activated NVM bit cell circuits R₀₀-R_(nm) in the same memory column C₀-C_(m). Current I₀-I_(m) flows from a respective source line SL₀-SL_(M) to output nodes 1108(0)-1108(m) as a function of the respective line voltage V₀-V_(m) driven by the bit line driver circuit 1006(0)-1006(m) to the NVM bit cell circuits R₀₀-R_(nm) in their respective memory column C₀-C_(m) divided by the parallel channel resistances of the NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). As shown in FIG. 11, each NVM bit cell circuit R₀₀-R_(nm) in an NVM storage string circuit 1102(0)-1102(m) comprises a source node (or drain node) coupled to a corresponding bit line BL₀-BL_(m) and a drain node (or source node) coupled to a corresponding source line SL₀-SL_(m) to be configured to be coupled in parallel with other NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). Thus, for example, current I₀ flowing on a respective source line SL₀ to the output node 1008(0) is a function of the sum of the dot products, meaning a respective input vector X₀-X_(n) multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n) in their respective, corresponding memory column C₀-C_(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1100 is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{BL}/R_{ij}}}$

-   -   where:         -   i=memory column 0 to m;         -   j=memory row 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=channel resistance of an NVM bit cell circuit.

If the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 1108(0)-1108(m) are coupled to a post-neuron layer, the NVM matrix circuit 1100 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

where: ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   R_(ij)=channel resistance of an NVM bit cell circuit; and     -   S=value at source lines of NVM storage string circuits.

FIG. 12 illustrates an NVM matrix circuit 1200 that is a reconfiguration of the NVM matrix circuit 300 in FIG. 3A into an n×m matrix by switching the memory rows and columns to have memory rows R₀₋R_(n) and memory columns C₀₋C_(m). The NVM matrix circuit 1200 includes NVM storage string circuits 1202(0)-1202(m) in the form of AND NVM FeFET circuits in this example, which are provided in respective memory columns C₀₋C_(m) to provide NVM bit cell circuits R₀₀₋R_(nm). Thus, each NVM bit cell circuit R₀₀₋R_(nm) is an NVM FeFET circuit. The word lines WL₀₋WL_(n) and bit lines BL₀₋BL_(m) are reversed between memory rows R₀₋R_(n) and columns C₀₋C_(m) from the NVM matrix circuit 300 in FIG. 3A, but are still coupled to the NVM bit cell circuits R₀₀₋R_(nm) in the same manner as in the NVM matrix circuit 300 in FIG. 3A. In this regard, as shown in FIG. 12, word lines WL₀₋WL_(n) that receive input vector X₀-X_(n) in the form of input voltages are provided for each memory row R₀₋R_(n). The bit lines BL₀₋BL_(m) are provided for each memory column C₀₋C_(m). Common components between the NVM matrix circuit 300 in FIG. 3A and the NVM matrix circuit 1200 in FIG. 12 are shown with common element numbers and thus will not be re-described. Read and write operations similar to that described above with regard to the NVM matrix circuit 300 can be performed in the NVM matrix circuit 1200 in FIG. 12.

Each NVM bit cell circuit R₀₀₋R_(nm) has a channel resistance representing a stored memory state. The channel resistances of the NVM bit cell circuits R₀₀-R_(nm) represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(nm) has a transistor comprising a gate node G₀₀-G_(nm) that is coupled to a respective word line WL₀-WL_(n) based on in which memory row R₀-R_(n) the NVM bit cell circuit R₀₀-R_(nm) is located. Each NVM bit cell circuit R₀₀-R_(nm) is configured to activate its semiconductor channel to couple its channel resistance (i.e., conductance) between the respective bit lines BL₀-BL_(m) and the respective source lines SL₀-SL_(m) in parallel with other activated NVM bit cell circuit R₀₀-R_(nm) in the same memory column C₀-C_(m). Current I₀-I_(m) flows from a respective source line SL₀-SL_(m) to output nodes 1208(0)-1208(m) as a function of the respective line voltage V₀-V_(m) driven to the NVM bit cell circuits R₀₀-R_(nm) in their respective memory column C₀-C_(m) divided by the parallel channel resistances of the NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). As shown in FIG. 12, each NVM bit cell circuit R₀₀-R_(nm) in an NVM storage string circuit 1202(0)-1202(m) comprises a source node (or drain node) coupled to a corresponding bit line BL₀-BL_(m) and a drain node (or source node) coupled to a corresponding source line SL₀-SL_(m) to be configured to be coupled in parallel with other NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). Thus, for example, current I₀ flowing on a respective source line SL₀ to the output node 1208(0) is a function of the sum of the dot product multiplications, meaning a respective input vector X₀-X_(n) multiplied by the corresponding memory states in NVM bit cell circuits R₀₀-R_(0n) in their respective, corresponding memory column C₀-C_(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1200 is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{BL}/R_{ij}}}$

-   -   where:         -   i=memory column 0 to m;         -   j=memory row 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=channel resistance of an NVM bit cell circuit.

If the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 1208(0)-1208(m) are coupled to a post-neuron layer, the NVM matrix circuit 1200 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(nm) by supporting backwards propagation of a weight update according to the following formula:

where: ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   R_(ij)=channel resistance of an NVM bit cell circuit; and     -   S=value at source lines of NVM storage string circuits.

FIG. 13 illustrates an NVM matrix circuit 1300 that is also a reconfiguration of the NVM matrix circuit 300 in FIG. 3A into an n×m matrix by switching the memory rows and columns to have memory row R₀₋R_(n) and memory columns C₀₋C_(m). The NVM matrix circuit 1300 includes NVM storage string circuits 1302(0)-1302(m) in the form of AND NVM magneto-resistive random access memory (MRAM) circuits in this example, which are provided in respective memory columns C₀₋C_(m) to provide NVM bit cell circuits R₀₀₋R_(nm). Thus, each NVM bit cell circuit R₀₀₋R_(nm) is an NVM MRAM circuit. The word lines WL₀₋WL_(n) and bit lines BL₀₋BL_(m) are reversed between memory rows R₀₋R_(n) and columns C₀₋C_(m) from the NVM matrix circuit 300 in FIG. 3A, but are still coupled to the NVM bit cell circuits R₀₀₋R_(nm) in the same manner as in the NVM matrix circuit 300 in FIG. 3A. In this regard, as shown in FIG. 13, word lines WL₀₋WL_(n) that receive input vectors X₀-X_(n) in the form of input voltages are provided for each memory row R₀₋R_(n). The bit lines BL₀₋BL_(m) are provided for each memory column C₀₋C_(m). Common components between the NVM matrix circuit 300 in FIG. 3A and the NVM matrix circuit 1300 in FIG. 13 are shown with common element numbers and thus will not be re-described. Read and write operations similar to that described above with regard to the NVM matrix circuit 300 can be performed in the NVM matrix circuit 1300 in FIG. 13.

Each NVM bit cell circuit R₀₀₋R_(nm) has a resistance representing a stored memory state. In this example, the resistances of the NVM bit cell circuits R₀₀₋R_(nm) are a function of whether a magnetic tunnel junction (MTJ) in the NVM bit cell circuits R₀₀₋R_(nm) are in a parallel (P) or anti-parallel (AP) magnetization state representing a memory state. The resistances of the NVM bit cell circuits R₀₀-R_(nm) represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(nm) has a transistor comprising a gate node G₀₀-G_(nm) that is coupled to a respective word line WL₀-WL_(n) based on in which memory row R₀-R_(n) the NVM bit cell circuit R₀₀-R_(nm) is located. Each NVM bit cell circuit R₀₀-R_(nm) is configured to activate its semiconductor channel to couple the MTJ resistance (i.e., conductance) between the respective bit lines BL₀-BL_(m) and the respective source line SL₀-SL_(m) in parallel with other activated NVM bit cell circuits R₀₀-R_(nm) in the same memory column C₀-C_(m). Current I₀-I_(m) flows from a respective source line SL₀-SL_(M) to output nodes 1308(0)-1308(m) as a function of the respective line voltage V₀-V_(m) driven to the NVM bit cell circuits R₀₀-R_(nm) in their respective memory column C₀-C_(m) divided by the parallel channel resistances of the NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). As shown in FIG. 13, each NVM bit cell circuit R₀₀-R_(nm) in an NVM storage string circuit 1302(0)-1302(m) comprises a source node (or drain node) coupled to a corresponding bit line BL₀-BL_(m) and a drain node (or source node) coupled to a corresponding source line SL₀-SL_(m) to be configured to be coupled in parallel with other NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). Thus for example, current I₀ flowing on a respective source line SL₀ to the output node 1308(0) is a function of the sum of the dot product multiplications, meaning a respective input vector X₀-X_(n) is multiplied by the corresponding memory states in NVM bit cell circuits R₀₀-R_(0n) in their respective, corresponding memory column C₀-C_(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1300 is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{BL}/R_{ij}}}$

-   -   where:         -   i=memory column 0 to m;         -   j=memory row 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=channel resistance of an NVM bit cell circuit.

If the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 1308(0)-1308(m) are coupled to a post-neuron layer, the NVM matrix circuit 1300 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   R_(ij)=channel resistance of an NVM bit cell circuit; and         -   S=value at source lines of NVM storage string circuits.

FIG. 14 illustrates another NVM matrix circuit 1400 that is also a reconfiguration of the NVM matrix circuit 300 in FIG. 3A into an n×m matrix by switching the memory rows and columns to have memory row R₀₋R_(n) and memory columns C₀₋C_(m). The NVM matrix circuit 1400 includes NVM storage string circuits 1402(0)-1402(m) in the form of AND NVM resistive random access memory (RRAM) circuits in this example, which are provided in respective memory columns C₀₋C_(m) to provide NVM bit cell circuits R₀₀₋R_(nm). Thus, each NVM bit cell circuit R₀₀₋R_(nm) is an NVM RRAM circuit. The word lines WL₀₋WL_(n) and bit lines BL₀₋BL_(m) are reversed between memory rows R₀₋R_(n) and columns C₀₋C_(m) from the NVM matrix circuit 300 in FIG. 3A, but are still coupled to the NVM bit cell circuits R₀₀₋R_(nm) in the same manner as in the NVM matrix circuit 300 in FIG. 3A. In this regard, as shown in FIG. 14, word lines WL₀₋WL_(n) that receive input vectors X₀-X_(n) in the form of input voltages are provided for each memory row R₀₋R_(n). The bit lines BL₀₋BL_(m) are provided for each memory column C₀₋C_(m). Common components between the NVM matrix circuit 300 in FIG. 3A and the NVM matrix circuit 1400 in FIG. 14 are shown with common element numbers and thus will not be re-described. Read and write operations similar to that described above with regard to the NVM matrix circuit 300 can be performed in the NVM matrix circuit 1400 in FIG. 14.

Each NVM bit cell circuit R₀₀₋R_(nm) has a resistance representing a stored memory state. In this example, the resistances of the NVM bit cell circuits R₀₀₋R_(nm) are a function of the resistance of the NVM bit cell circuits R₀₀₋R_(nm) based on their memory state. The resistances of the NVM bit cell circuits R₀₀-R_(nm) represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(nm) has a transistor comprising a gate node G₀₀-G_(nm) that is coupled to a respective word line WL₀-WL_(n) based on in which memory row R₀-R_(n) the NVM bit cell circuit R₀₀-R_(nm) is located. Each NVM bit cell circuit R₀₀-R_(nm) is configured to activate its semiconductor channel to couple the MTJ resistance (i.e., conductance) between the respective bit lines BL₀-BL_(m) and the respective source lines SL₀-SL_(m) in parallel with other activated NVM bit cell circuit R₀₀-R_(nm) in the same memory column C₀-C_(m). Current I₀-I_(m) flows from a respective source line SL₀-SL_(m) to output nodes 1408(0)-1408(m) as a function of the respective line voltage V₀-V_(m) driven to the NVM bit cell circuits R₀₀-R_(nm) in their respective memory column C₀-C_(m) divided by the parallel channel resistances of the NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). As shown in FIG. 14, each NVM bit cell circuit R₀₀-R_(nm) in an NVM storage string circuit 1402(0)-1402(m) comprises a source node (or drain node) coupled to a corresponding bit line BL₀-BL_(m) and a drain node (or source node) coupled to a corresponding source line SL₀-SL_(m) to be configured to be coupled in parallel with other NVM bit cell circuits R₀₀-R_(nm) in a respective memory column C₀-C_(m). Thus for example, current I₀ flowing on a respective source line SL₀ to the output node 1408(0) is a function of the sum of the dot product multiplications, meaning a respective input vector X₀-X_(n) is multiplied by the corresponding memory states in NVM bit cell circuits R₀₀-R_(0n) in their respective, corresponding memory column C₀-C_(m). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1400 is configured to produce currents I₀-I_(m) on an input layer according to the following formula:

$I_{j} = {\sum\limits_{i}\; {V_{BL}/R_{ij}}}$

-   -   where:         -   i=memory column 0 to m;         -   j=memory row 0 to n;         -   V_(BL)=voltage V_(i); and         -   R_(ij)=channel resistance of an NVM bit cell circuit.

If the word lines WL₀-WL_(m) are coupled to a pre-neuron layer and the output nodes 1408(0)-1408(m) are coupled to a post-neuron layer, the NVM matrix circuit 1400 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

where: ΔR _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   R_(ij)=channel resistance of an NVM bit cell circuit; and     -   S=value at source lines of NVM storage string circuits.

FIG. 15 is a schematic diagram of another exemplary NVM matrix circuit 1500 that can perform matrix multiplication without the use of cross-bar connections employing OR-based NVM storage string circuits 1502(0)-1502(m) provided as NOR NVM flash circuits in this example. In this manner, as discussed below, the summed channel conductances affect the currents I₀-I_(m) to flow to output nodes 1508(0)-1508(m) representing dot product matrix multiplication calculations. In this regard, the NVM matrix circuit 1500 employs NVM storage string circuits 1502(0)-1502(m) in ‘m+1’ memory rows R₀-R_(m) that each include a plurality of NVM bit cell circuits R₀₀-R_(mn). Thus, the NVM bit cell circuits R₀₀-R_(mn) are arranged in memory rows R₀-R_(m) and memory columns C₀-C_(n). The NVM matrix circuit 1500 includes a respective word line WL₀-WL_(m) for each memory row R₀-R_(m). Word line driver circuits 1506(0)-1506(m) are provided that are each configured to drive a respective voltage V₀-V_(m) on the respective word lines WL₀-WL_(m). Source lines SL₀-SL_(m) for each NVM storage string circuit 1502(0)-1502(m) include respective output nodes 1508(0)-1508(m). The source lines SL₀-SL_(m) are configured to provide a respective current I₀-I_(m) to the respective output nodes 1508(0)-1508(m) to be provided as an output vector S₀-S_(m). For example, the output vector S₀-S_(m) may be a binary post-synapse vector. The NVM matrix circuit 1500 also includes a respective bit line BL₀-BL_(n) for each memory column C₀-C_(n) in this example. For example, the input vector X₀-X_(n) may be a binary pre-synapse vector. Bit line driver circuits 1510(0)-1510(n) are provided that are each configured to drive a respective input vector X₀-X_(n) in the form of input voltages on the respective bit lines BL₀-BL_(n) in this example. Note however that alternatively, the word lines WL₀₋WL_(m) provided in the respective memory rows R₀₋R_(m) could be configured to receive the input vector X, and respective fixed voltages be applied to the bit lines BL₀₋BL_(n) in the respective memory columns C₀₋C_(n) with the respective voltages V₀-V_(m) applied.

With continuing reference to FIG. 15, each NVM bit cell circuit R₀₀-R_(mn) has a conductance representing a stored memory state. The series conductances of the NVM bit cell circuits R₀₀-R_(mn) in FIG. 15 represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(mn) in this example has a transistor comprising a gate node G₀₀-G_(mn) that is coupled to a respective word line WL₀-WL_(m) based on which memory row R₀-R_(m) the NVM bit cell circuit R₀₀-R_(mn) is located. Each NVM bit cell circuit R₀₀-R_(mn) is configured to activate its respective semiconductor channel on a respective source line SL₀-SL_(m) to couple its conductance on the respective source line SL₀-SL_(m). The current I₀-I_(m) flowing from the respective NVM storage string circuits 1502(0)-1502(m) on the respective source lines SL₀-SL_(m) to output nodes 1508(0)-1508(m) is a function of the respective voltages V₀-V_(m) driven by the word line driver circuits 1506(0)-1506(m) on respective word lines WL₀-WL_(m) divided by the summed conductances of the NVM bit cell circuits R₀₀-R_(mn). Thus for example, current I₀ flowing on a respective source line SL₀ to the output node 1508(0) is a function of the sum of the dot product multiplications, meaning an input vector X₀-X_(n) is multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1500 is configured to produce currents I₀-I_(m) according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{{BL},j} \cdot G_{ij}}}$

-   -   where:         -   i=memory row 0 to m;         -   j=memory column 0 to n;         -   V_(BL)=voltage V_(j); and         -   G_(ij)=conductance of an NVM bit cell circuit.

The conductances G_(ij) of the respective NVM bit cell circuits R₀₀-R_(mn) correlate to the voltages V₀-V_(m) applied to the word lines WL₀-WL_(m). If the bit lines BL₀-BL_(n) are coupled to a pre-neuron layer and the output nodes 1508(0)-1508(m) are coupled to a post-neuron layer, the NVM matrix circuit 1500 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔG _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   G_(ij)=conductance of an NVM bit cell circuit; and         -   S=source lines of NVM storage string circuits.

Read and write operations similar to that described above with regard to the NVM matrix circuit 300 in FIG. 3A can be performed in the NVM matrix circuit 1500 in FIG. 15.

Other types of NVM bit cell circuits can be employed besides NOR flash circuits like shown in the NVM matrix circuit 1500 in FIG. 15. For example, FIG. 16 is a schematic diagram of another exemplary matrix circuit 1600 without need for cross-bar connections like the NVM matrix circuit 1500 in FIG. 15. However, the NVM matrix circuit 1600 in FIG. 16 includes NVM storage string circuits 1602(0)-1602(m) in the form of NOR NVM FeFET circuits. Each NVM storage string circuit 1602(0)-1602(m) includes an NVM matrix circuit R₀₀₋R_(mn) in the form of NVM Fe-FET circuits in this example. Common components between the NVM matrix circuit 1500 in FIG. 15 and the NVM matrix circuit 1600 in FIG. 16 are shown with common element numbers and thus will not be re-described. Read and write operations similar to that described above with regard to the NVM matrix circuit 300 in FIG. 3A can be performed in the NVM matrix circuit 1600 in FIG. 16.

FIG. 17 is a schematic diagram of another exemplary NVM matrix circuit 1700 that can perform matrix multiplication without the use of cross-bar connections employing OR-based NVM storage string circuits 1702(0)-1702(m) provided as NOR NVM MRAM circuits in this example. In this manner, as discussed below, the summed conductances of the MTJs in the NVM storage string circuits 1702(0)-1702(m) affect the currents I₀-I_(m) to flowing to output nodes 1708(0)-1708(m) representing dot product matrix multiplication calculations. In this regard, the NVM matrix circuit 1700 employs NVM storage string circuits 1702(0)-1702(m) in ‘m+1’ memory rows R₀-R_(m) that each include a plurality of NVM bit cell circuits R₀₀-R_(mn). Thus, the NVM bit cell circuits R₀₀-R_(mn) are arranged in memory rows R₀-R_(m) and memory columns C₀-C_(n). The NVM matrix circuit 1700 includes a respective word line WL₀-WL_(m) for each memory row R₀-R_(m). Word line driver circuits 1706(0)-1706(m) are provided that are each configured to drive a respective voltage V₀-V_(m) on the respective word lines WL₀-WL_(m). Source lines SL₀-SL_(m) for each NVM storage string circuit 1702(0)-1702(m) include respective output nodes 1708(0)-1708(m). The source lines SL₀-SL_(m) are configured to provide a respective current I₀-I_(m) to the respective output nodes 1708(0)-1708(m) to be provided as an output vector S₀-S_(m). For example, the output vector S₀-S_(m) may be a binary post-synapse vector. The NVM matrix circuit 1700 also includes a respective bit line BL₀-BL_(n) for each memory column C₀-C_(n) in this example. Bit line driver circuits 1710(0)-1710(n) are provided that are each configured to drive a respective input vector X₀-X_(n) in the form of input voltages on the respective bit lines BL₀-BL_(n) in this example. Note however that alternatively, the word lines WL₀₋WL_(m) provided in the respective memory rows R₀₋R_(m) could be configured to receive the input vector X, and respective fixed voltages be applied to the bit lines BL₀₋BL_(n) in the respective memory columns C₀₋C_(n) with the respective voltages V₀-V_(m) applied. For example, the input vector X₀-X_(n) may be a binary pre-synapse vector.

With continuing reference to FIG. 17, each NVM bit cell circuit R₀₀-R_(mn) has a conductance representing a stored memory state. The series conductances of the NVM bit cell circuits R₀₀-R_(mn) in FIG. 17 represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(mn) in this example has a transistor comprising a gate node G₀₀-G_(mn) that is coupled to a respective word line WL₀-WL_(m) based on which memory row R₀-R_(m) the NVM bit cell circuit R₀₀-R_(mn) is located. Each NVM bit cell circuit R₀₀-R_(mn) is configured to activate its respective semiconductor channel on a respective source line SL₀-SL_(m) to couple the conductance of its respective MTJ on the respective source line SL₀-SL_(m). The current I₀-I_(m) flowing from the respective NVM storage string circuits 1702(0)-1702(m) on the respective source lines SL₀-SL_(m) to output nodes 1708(0)-1708(m) is a function of the respective voltages V₀-V_(m) driven by word line driver circuits 1706(0)-1706(m) on respective word lines WL₀-WL_(m) divided by the summed conductances of the NVM bit cell circuits R₀₀-R_(mn). Thus for example, current I₀ flowing on a respective source line SL₀ to the output node 1708(0) is a function of the sum of the dot product multiplications, meaning input vector X₀-X_(n) is multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n). The currents I₀-I_(m) may be analog representations of a summation of the dot product multiplications which can be converted to binary values. In other words, the NVM matrix circuit 1700 is configured to produce currents I₀-I_(m) according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{{BL},j} \cdot G_{ij}}}$

-   -   where:         -   i=memory row 0 to m;         -   j=memory column 0 to n;         -   V_(BL)=voltage V_(j); and         -   G_(ij)=conductance of an NVM bit cell circuit.

The conductances G_(ij) of the respective NVM bit cell circuits R₀₀-R_(mn) correlate to the voltages V₀-V_(m) applied to the word lines WL₀-WL_(m). If the bit lines BL₀-BL_(n) are coupled to a pre-neuron layer and the output nodes 1708(0)-1708(m) are coupled to a post-neuron layer, the NVM matrix circuit 1700 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔG _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   G_(ij)=conductance of an NVM bit cell circuit; and         -   S=source lines of NVM storage string circuits.

FIG. 18 is a schematic diagram of another exemplary NVM matrix circuit 1800 that can perform matrix multiplication without the use of cross-bar connections employing OR-based NVM storage string circuits 1802(0)-1802(m) provided as NOR NVM RRAM circuits in this example. In this manner, as discussed below, the summed conductances of the NVM storage string circuits 1802(0)-1802(m) affect the currents I₀-I_(m) to flowing to output nodes 1808(0)-1808(m) representing dot product matrix multiplication calculations. In this regard, the NVM matrix circuit 1800 employs NVM storage string circuits 1802(0)-1802(m) in ‘m+1’ memory rows R₀-R_(m) that each include a plurality of NVM bit cell circuits R₀₀-R_(mn). Thus, the NVM bit cell circuits R₀₀-R_(mn) are arranged in memory rows R₀-R_(m) and memory columns C₀-C_(n). The NVM matrix circuit 1800 includes a respective word line WL₀-WL_(m) for each memory row R₀-R_(m). Word line driver circuits 1806(0)-1806(m) are provided that are each configured to drive a respective voltage V₀-V_(m) on the respective word lines WL₀-WL_(m). Source lines SL₀-SL_(m) for each NVM storage string circuit 1802(0)-1802(m) include respective output nodes 1808(0)-1808(m). The source lines SL₀-SL_(m) are configured to provide a respective current I₀-I_(m) to the respective output nodes 1808(0)-1808(m) to be provided as an output vector S₀-S_(m). For example, the output vector S₀-S_(m) may be a binary post-synapse vector. The NVM matrix circuit 1800 also includes a respective bit line BL₀-BL_(n) for each memory column C₀-C_(n) in this example. Bit line driver circuits 1810(0)-1810(n) are provided that are each configured to drive a respective input vector X₀-X_(n) in the form of input voltages on the respective bit lines BL₀-BL_(n) in this example. Note however that alternatively, the word lines WL₀₋WL_(m) provided in the respective memory rows R₀₋R_(m) could be configured to receive the input vector X, and respective fixed voltages be applied to the bit lines BL₀₋BL_(n) in the respective memory columns C₀₋C_(n) with the respective voltages V₀-V_(m) applied. For example, the input vector X₀-X_(n) may be a binary pre-synapse vector.

With continuing reference to FIG. 18, each NVM bit cell circuit R₀₀-R_(mn) has a conductance representing a stored memory state. The series conductances of the NVM bit cell circuits R₀₀-R_(mn) in FIG. 18 represent a weight matrix. Each NVM bit cell circuit R₀₀-R_(mn) in this example has a transistor comprising a gate node G₀₀-G_(mn) that is coupled to a respective word line WL₀-WL_(m) based on which memory row R₀-R_(m) the NVM bit cell circuit R₀₀-R_(mn) is located. Each NVM bit cell circuit R₀₀-R_(mn) is configured to activate its respective semiconductor channel on a respective source line SL₀-SL_(m) to couple the conductance of its respective MTJ on the respective source line SL₀-SL_(m). The current I₀-I_(m) flowing from the respective NVM storage string circuits 1802(0)-1802(m) on the respective source lines SL₀-SL_(m) to output nodes 1808(0)-1808(m) is a function of the respective voltages V₀-V_(m) driven by the word line driver circuits 1806(0)-1806(m) on respective word lines WL₀-WL_(m) divided by the summed conductances of the NVM bit cell circuits R₀₀-R_(mn). Thus for example, current I₀ flowing on a respective source line SL₀ to the output node 1808(0) is a function of the sum of the dot product multiplications, meaning input vector X₀-X_(n) is multiplied by the corresponding memory states in the NVM bit cell circuits R₀₀-R_(0n). The currents I₀-I_(m) may be analog representations of a summation of the dot products which can be converted to binary values. In other words, the NVM matrix circuit 1800 is configured to produce currents I₀-I_(m) according to the following formula:

$I_{i} = {\sum\limits_{j}\; {V_{{BL},j} \cdot G_{ij}}}$

-   -   where:         -   i=memory row 0 to m;         -   j=memory column 0 to n;         -   V_(BL)=voltage V_(j); and         -   G_(ij)=conductance of an NVM bit cell circuit.

The conductances G_(ij) of the respective NVM bit cell circuits R₀₀-R_(mn) correlate to the voltages V₀-V_(m) applied to the word lines WL₀-WL_(m). If the bit lines BL₀-BL_(n) are coupled to a pre-neuron layer and the output nodes 1808(0)-1808(m) are coupled to a post-neuron layer, the NVM matrix circuit 1800 is also configured to train the channel resistance of the NVM bit cell circuits R₀₀-R_(mn) by supporting backwards propagation of a weight update according to the following formula:

ΔG _(ij) =η·S _(post,i) ·S _(post+1,j)

-   -   where:         -   G_(ij)=conductance of an NVM bit cell circuit; and         -   S=source lines of NVM storage string circuits.

FIG. 19 is a block diagram of an exemplary chip package 1900 that can include a dedicated matrix circuit chip 1902 that has an NVM matrix circuit 1904 for performing matrix computations without need for cross-bar connections and according to aspects disclosed herein including without limitation the NVM matrix circuits in FIGS. 3A-18. In this regard, a system-on-a-chip (SoC) 1906 may be included that can contain a microprocessor and other supporting circuitry to provide a computer system. An external system memory chip 1908, such as a dynamic RAM (DRAM) memory chip may be provided in the chip package 1900 and coupled to the SoC 1906 through through-silicon vias (TSVs) 1910. The dedicated matrix circuit chip 1902 may also be coupled to the SoC 1906 through the TSVs 1910. Solder bumps 1912 may be provided on the SoC 1906 to be able to solder-bond the chip package 1900 to a circuit board. The system memory chip 1908 could be connected to the dedicated matrix circuit chip 1902 through a dedicated local bus to improve performance. The dedicated matrix circuit chip 1902 could also be embedded into the SoC 1906 to save power and improve performance.

In another aspect, an NVM matrix circuit may be provided that includes a plurality of means for applying a plurality of input voltages representing an input vector. As non-limiting examples, the means for applying a plurality of input voltages representing an input vector may be the word lines WL₀-WL_(n) in the NVM matrix circuit 300 in FIGS. 3A-7B, the word lines WL₀-WL_(n) in the NVM matrix circuit 1100 in FIG. 11, the word lines WL₀-WL_(n) in the NVM matrix circuit 1200 in FIG. 12, the word lines WL₀-WL_(n) in the NVM matrix circuit 1300 in FIG. 13, the word lines WL₀-WL_(n) in the NVM matrix circuit 1400 in FIG. 14, the word lines WL₀-WL_(m) in the NVM matrix circuit 1500 in FIG. 15, the word lines WL₀-WL_(m) in the NVM matrix circuit 1600 in FIG. 16, the word lines WL₀-WL_(m) in the NVM matrix circuit 1700 in FIG. 17, or the word lines WL₀-WL_(m) in the NVM matrix circuit 1800 in FIG. 18.

The NVM matrix circuit may also include a plurality of means for applying a plurality of line voltages. As non-limiting examples, the means for applying a plurality of line voltages may be the bit lines BL₀-BL_(m) in the NVM matrix circuit 300 in FIGS. 3A-7B, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1100 in FIG. 11, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1200 in FIG. 12, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1300 in FIG. 13, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1400 in FIG. 14, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1500 in FIG. 15, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1600 in FIG. 16, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1700 in FIG. 17, or the bit lines BL₀-BL_(n) in the NVM matrix circuit 1800 in FIG. 18. As other non-limiting examples, the means for applying a plurality of line voltages may be the source lines SL₀-SL_(m) in the NVM matrix circuit 300 in FIGS. 3A-7B, the source lines SL₀-SL_(m) in the NVM matrix circuit 1100 in FIG. 11, the source lines SL₀-SL_(m) in the NVM matrix circuit 1200 in FIG. 12, the source lines SL₀-SL_(m) in the NVM matrix circuit 1300 in FIG. 13, the source lines SL₀-SL_(m) in the NVM matrix circuit 1400 in FIG. 14, the source lines SL₀-SL_(n) in the NVM matrix circuit 1500 in FIG. 15, the source lines SL₀-SL_(n) in the NVM matrix circuit 1600 in FIG. 16, the source lines SL₀-SL_(n) in the NVM matrix circuit 1700 in FIG. 17, or the source lines SL₀-SL_(n) in the NVM matrix circuit 1800 in FIG. 18.

The NVM matrix circuit may also include a plurality of means for providing a plurality of output currents representing an output vector. As non-limiting examples, the means for providing a plurality of output currents may be the source lines SL₀-SL_(m) in the NVM matrix circuit 300 in FIGS. 3A-7B, the source lines SL₀-SL_(m) in the NVM matrix circuit 1100 in FIG. 11, the source lines SL₀-SL_(m) in the NVM matrix circuit 1200 in FIG. 12, the source lines SL₀-SL_(m) in the NVM matrix circuit 1300 in FIG. 13, the source lines SL₀-SL_(m) in the NVM matrix circuit 1400 in FIG. 14, the source lines SL₀-SL_(n) in the NVM matrix circuit 1500 in FIG. 15, the source lines SL₀-SL_(n) in the NVM matrix circuit 1600 in FIG. 16, the source lines SL₀-SL_(n) in the NVM matrix circuit 1700 in FIG. 17, or the source lines SL₀-SL_(n) in the NVM matrix circuit 1800 in FIG. 18. As other non-limiting examples, the means for providing a plurality of output currents may be the bit lines BL₀-BL_(m) in the NVM matrix circuit 300 in FIGS. 3A-7B, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1100 in FIG. 11, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1200 in FIG. 12, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1300 in FIG. 13, the bit lines BL₀-BL_(m) in the NVM matrix circuit 1400 in FIG. 14, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1500 in FIG. 15, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1600 in FIG. 16, the bit lines BL₀-BL_(n) in the NVM matrix circuit 1700 in FIG. 17, or the bit lines BL₀-BL_(n) in the NVM matrix circuit 1800 in FIG. 18.

The NVM matrix circuit may also include a plurality of NVM storage string means each electrically coupled to a corresponding means for applying an input voltage among the plurality of means for applying the plurality of input voltages and a corresponding means for providing an output current among the plurality of means for providing the plurality of output currents. As non-limiting examples, the plurality of NVM storage string means may include the NVM storage string circuits 302(0)-302(m) in FIGS. 3A-7B, the NVM storage string circuits 1002(0)-1002(m) in FIG. 10, the NVM storage string circuits 1102(0)-1102(m) in FIG. 11, the NVM storage string circuits 1202(0)-1202(m) in FIG. 12, the NVM storage string circuits 1302(0)-1302(m) in FIG. 13, the NVM storage string circuits 1402(0)-1402(m) in FIG. 14, the NVM storage string circuits 1502(0)-1502(n) in FIG. 15, the NVM storage string circuits 1602(0)-1602(n) in FIG. 16, the NVM storage string circuits 1702(0)-1702(n) in FIG. 17, or the NVM storage string circuits 1802(0)-1802(n) in FIG. 18.

Each of the plurality of NVM storage string means may comprise a plurality of NV means for storing a memory state each having a resistance representing the stored memory state to form a data vector for a corresponding NVM storage string means, each plurality of plurality NV means for storing the memory state, and comprising a means for electrically coupling the resistance of the NV means for storing the memory state to a means for providing the output current among the plurality of means for providing the plurality of output currents; and a means for controlling coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents. As non-limiting examples, the plurality of NV means for storing a memory state may include the NVM bit cell circuits R₀₀-R_(mn) in FIGS. 3A-7B, the NVM bit cell circuits R₀₀-R_(mn) in FIG. 10, the NVM bit cell circuits R₀₀-R_(mn) in FIG. 11, the NVM bit cell circuits R₀₀-R_(nm) in FIG. 12, the NVM bit cell circuits R₀₀-R_(nm) in FIG. 13, the NVM bit cell circuits R₀₀-R_(nm) in FIG. 14, the NVM bit cell circuits R₀₀-R_(mn) in FIG. 15, the NVM bit cell circuits R₀₀-R_(mn) in FIG. 16, the NVM bit cell circuits R₀₀-R_(mn) in FIG. 17, or the NVM bit cell circuits R₀₀-R_(mn) in FIG. 18.

The NVM matrix circuit may also include a plurality of access means for controlling the means for electrically coupling the corresponding means for applying the input voltage among the plurality of means for applying the plurality of input voltages to a corresponding NVM storage string means in the coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents. Non-limiting examples of the plurality of access means include the access transistor(s) 312(0)-312(m), 318(0)-318(m) in the NVM matrix circuit 300 in FIGS. 3A and 4A-7B or the access transistor(s) 312(0)-312(m), 1018(0)-1018(m) in the NVM matrix circuit 1000 in FIG. 10.

NVM matrix circuits employing NVM matrix circuits for performing matrix computations without need for cross-bar connections and according to aspects disclosed herein, may be provided in or integrated into any processor-based device. Examples, without limitation, include a set top box, an entertainment unit, a navigation device, a communications device, a fixed location data unit, a mobile location data unit, a global positioning system (GPS) device, a mobile phone, a cellular phone, a smart phone, a session initiation protocol (SIP) phone, a tablet, a phablet, a server, a computer, a portable computer, a mobile computing device, a wearable computing device (e.g., a smart watch, a health or fitness tracker, eyewear, etc.), a desktop computer, a personal digital assistant (PDA), a monitor, a computer monitor, a television, a tuner, a radio, a satellite radio, a music player, a digital music player, a portable music player, a digital video player, a video player, a digital video disc (DVD) player, a portable digital video player, an automobile, a vehicle component, avionics systems, a drone, and a multicopter.

In this regard, FIG. 20 illustrates an example of a processor-based system 2000 that can be included in an IC 2002. The processor-based system 2000 can include NVM matrix circuits 2004 employing NVM bit cell circuits for performing matrix computations without need for cross-bar connections and according to any aspects disclosed herein. The IC 2002 may be included in or provided as a SoC 2006. The processor-based system 2000 includes a CPU 2008 that includes one or more processors 2010. The CPU 2008 may have a cache memory 2012 coupled to the processor(s) 2010 for rapid access to temporarily stored data. The cache memory 2012 can include the NVM matrix circuits 2004 according to any of the examples disclosed herein. The CPU 2008 is coupled to a system bus 2014 and can intercouple master and slave devices included in the processor-based system 2000. As is well known, the CPU 2008 communicates with these other devices by exchanging address, control, and data information over the system bus 2014. Although not illustrated in FIG. 20, multiple system buses 2014 could be provided, wherein each system bus 2014 constitutes a different fabric. For example, the CPU 2008 can communicate bus transaction requests to a memory system 2016 as an example of a slave device. The memory system 2016 may include a memory array 2018 that includes memory bit cells 2020. The memory bit cells 2020 may be MRAM bit cells for example. The memory array 2018 can include the NVM matrix circuits 2004.

Other master and slave devices can be connected to the system bus 2014. As illustrated in FIG. 20, these devices can include the memory system 2016, and one or more input devices 2022. The input device(s) 2022 can include any type of input device, including but not limited to input keys, switches, voice processors, etc. The other devices can also include one or more output devices 2024, and one or more network interface devices 2026. The output device(s) 2024 can include any type of output device, including but not limited to audio, video, other visual indicators, etc. The other devices can also include one or more display controllers 2030 as examples. The network interface device(s) 2026 can be any devices configured to allow exchange of data to and from a network 2028. The network 2028 can be any type of network, including but not limited to a wired or wireless network, a private or public network, a local area network (LAN), a wireless local area network (WLAN), a wide area network (WAN), a BLUETOOTH™ network, and the Internet. The network interface device(s) 2026 can be configured to support any type of communications protocol desired.

The CPU 2008 may also be configured to access the display controller(s) 2030 over the system bus 2014 to control information sent to one or more displays 2032. The display controller 2030 can include the NVM matrix circuits 2004. The display controller(s) 2030 sends information to the display(s) 2032 to be displayed via one or more video processors 2034, which process the information to be displayed into a format suitable for the display(s) 2032. The display(s) 2032 can include any type of display, including but not limited to a cathode ray tube (CRT), a liquid crystal display (LCD), a plasma display, etc.

Those of skill in the art will further appreciate that the various illustrative logic blocks, modules, circuits, and algorithms described in connection with the aspects disclosed herein may be implemented as electronic hardware, instructions stored in memory or in another computer readable medium and executed by a processor or other processing device, or combinations of both. The master devices and slave devices described herein may be employed in any circuit, hardware component, integrated circuit (IC), or IC chip, as examples. Memory disclosed herein may be any type and size of memory and may be configured to store any type of information desired. To clearly illustrate this interchangeability, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. How such functionality is implemented depends upon the particular application, design choices, and/or design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.

The various illustrative logic blocks, modules, and circuits described in connection with the aspects disclosed herein may be implemented or performed with a processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices (e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration).

The aspects disclosed herein may be embodied in hardware and in instructions that are stored in hardware, and may reside, for example, in Random Access Memory (RAM), flash memory, Read Only Memory (ROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), registers, a hard disk, a removable disk, a CD-ROM, or any other form of computer readable medium known in the art. An exemplary storage medium is coupled to the processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a remote station. In the alternative, the processor and the storage medium may reside as discrete components in a remote station, base station, or server.

It is also noted that the operational steps described in any of the exemplary aspects herein are described to provide examples and discussion. The operations described may be performed in numerous different sequences other than the illustrated sequences. Furthermore, operations described in a single operational step may actually be performed in a number of different steps. Additionally, one or more operational steps discussed in the exemplary aspects may be combined. It is to be understood that the operational steps illustrated in the flowchart diagrams may be subject to numerous different modifications as will be readily apparent to one of skill in the art. Those of skill in the art will also understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

The previous description of the disclosure is provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein. 

What is claimed is:
 1. A non-volatile (NV) memory (NVM) matrix circuit, comprising: a plurality of word lines configured to receive an input vector represented by an input voltage on each word line among the plurality of word lines; a plurality of bit lines, each bit line among the plurality of bit lines configured to receive a corresponding line voltage; a plurality of source lines; a plurality of NVM storage string circuits, each NVM storage string circuit among the plurality of NVM storage string circuits configured to be electrically coupled between a corresponding bit line among the plurality of bit lines and a corresponding source line among the plurality of source lines each comprising a plurality of NVM bit cell circuits; each NVM bit cell circuit among the plurality of NVM bit cell circuits having a resistance representing a stored memory state in the NVM bit cell circuit to form a data vector for the corresponding NVM storage string circuit; each NVM bit cell circuit among the plurality of NVM bit cell circuits in the NVM storage string circuit, comprising: a gate node coupled to a corresponding word line among the plurality of word lines; and each NVM bit cell circuit configured to couple its resistance to the source line in response to the input voltage applied to the corresponding word line coupled to the gate node; and a plurality of access transistors, each access transistor among the plurality of access transistors coupled to a corresponding bit line among the plurality of bit lines and a corresponding NVM storage string circuit among the plurality of NVM storage string circuits coupled to the source line corresponding to the bit line; each access transistor among the plurality of access transistors comprising an access gate node coupled to an access line; and each access transistor among the plurality of access transistors configured to electrically couple the corresponding bit line to the corresponding NVM storage string circuit in response to an access voltage applied to the access gate node.
 2. The NVM matrix circuit of claim 1, wherein none of the plurality of word lines are cross-connected to any of the plurality of bit lines.
 3. The NVM matrix circuit of claim 1, wherein each NVM bit cell circuit among the plurality of NVM bit cell circuits in the NVM storage string circuit further comprises a semiconductor channel configured to be electrically coupled to the source line to couple the channel resistance of the NVM bit cell circuit to the source line in response to the input voltage applied to the corresponding word line coupled to the gate node.
 4. The NVM matrix circuit of claim 1, further comprising a plurality of second access transistors, each second access transistor among the plurality of second access transistors coupled to a corresponding source line among the plurality of source lines and a corresponding NVM storage string circuit among the plurality of NVM storage string circuits; each second access transistor among the plurality of second access transistors comprising: a second access gate node coupled to a second access line; and a second semiconductor channel configured to electrically couple the corresponding source line to the corresponding NVM storage string circuit in response to the input voltage applied to the second access gate node.
 5. The NVM matrix circuit of claim 1, wherein an NVM storage string circuit among the plurality of NVM storage string circuits is configured to generate a respective current flowing through a source line among the plurality of source lines coupled to the NVM storage string circuit to a respective output node based on the line voltage applied to the bit line coupled to the NVM storage string circuit and the resistances applied by each of the plurality of NVM bit cell circuits of the NVM storage string circuit in response to a read activation voltage being applied to the gate nodes of each of the plurality of NVM bit cell circuits.
 6. The NVM matrix circuit of claim 5, wherein an amplitude of the current flowing through the source line represents a dot product multiplication of a data vector of the NVM bit cell circuit coupled to the source line, by the input vector.
 7. The NVM matrix circuit of claim 1, wherein each NVM storage string circuit among the plurality of NVM storage string circuits is configured to generate a respective current flowing through a source line coupled to the NVM storage string circuit to a respective output node based on the line voltage applied to the bit line coupled to the NVM storage string circuit and the resistances applied by each of the plurality of NVM bit cell circuits of the NVM storage string circuit in response to a read activation voltage being applied to the gate nodes of each of the plurality of NVM bit cell circuits.
 8. The NVM matrix circuit of claim 5, wherein amplitudes of each of the respective currents flowing through the plurality of source lines represents a dot product multiplication of data vectors of the respective NVM bit cell circuit coupled to the respective source line, by the input vector.
 9. The NVM matrix circuit of claim 1, wherein one or more NVM bit cell circuits in an NVM storage string circuit among the plurality of NVM storage string circuits is configured to write a memory state based on a write activation voltage applied to the gate node of the NVM bit cell circuit.
 10. The NVM matrix circuit of claim 9, wherein the one or more NVM bit cell circuits in the NVM storage string circuit among the plurality of NVM storage string circuits is further configured to write the memory state in response to a read activation voltage different from the write activation voltage and applied to the gate node of the NVM bit cell circuit in the NVM storage string circuit not being written.
 11. The NVM matrix circuit of claim 1, wherein the plurality of NVM storage string circuits each comprise a NAND NVM bit cell circuit comprising the plurality of NVM bit cell circuits configured to couple its resistance in series on the source line in response to the input voltage applied to its gate node.
 12. The NVM matrix circuit of claim 11, wherein each NVM bit cell circuit in a respective NVM storage string circuit among the plurality of NVM storage string circuits comprises a source node coupled to a drain node of an adjacent NVM bit cell circuit.
 13. The NVM matrix circuit of claim 11, wherein each NAND NVM bit cell circuit is comprised from the group consisting of a NAND NVM flash circuit and a NAND NVM Ferroelectric (Fe) Field-Effect Transistor (FET) (FeFET) circuit.
 14. The NVM matrix circuit of claim 1, wherein the plurality of NVM storage string circuits each comprise an AND NVM bit cell circuit comprising the plurality of NVM bit cell circuits configured to couple its resistance in parallel between its corresponding bit line and corresponding source line in response to the input voltage applied to its gate node.
 15. The NVM matrix circuit of claim 14, wherein each NVM bit cell circuit in a respective NVM storage string circuit among the plurality of NVM storage string circuits comprises a source node coupled to a drain node of an adjacent NVM bit cell circuit coupled to a bit line among the plurality of bit lines, and the drain node coupled to the source line coupled to the NVM storage string circuit.
 16. The NVM matrix circuit of claim 14, wherein each AND NVM bit cell circuit is comprised from the group consisting of an AND NVM flash circuit, an AND NVM FeFET circuit, an AND NVM magneto-resistive random access memory (MRAM) NVM circuit, and an AND NVM resistive random access memory (RRAM) circuit.
 17. The NVM matrix circuit of claim 1, wherein the plurality of NVM storage string circuits each comprise a NOR NVM bit cell circuit comprising the plurality of NVM bit cell circuits configured to couple its resistance to the respective source line in response to the input voltage applied to its gate node.
 18. The NVM matrix circuit of claim 17, wherein each NOR NVM bit cell circuit is comprised from the group consisting of a NOR NVM flash circuit, a NOR NVM FeFET circuit, a NOR NVM magneto-resistive random access memory (MRAM) circuit, and a NOR NVM resistive random access memory (RRAM) circuit.
 19. The NVM matrix circuit of claim 1 integrated into an integrated circuit (IC).
 20. The NVM matrix circuit of claim 1 integrated into a system-on-a-chip (SoC).
 21. The NVM matrix circuit of claim 1 integrated into a device selected from the group consisting of: a set top box; an entertainment unit; a navigation device; a communications device; a fixed location data unit; a mobile location data unit; a global positioning system (GPS) device; a mobile phone; a cellular phone; a smart phone; a session initiation protocol (SIP) phone; a tablet; a phablet; a server; a computer; a portable computer; a mobile computing device; a wearable computing device (e.g., a smart watch, a health or fitness tracker, eyewear, etc.); a desktop computer; a personal digital assistant (PDA); a monitor; a computer monitor; a television; a tuner; a radio; a satellite radio; a music player; a digital music player; a portable music player; a digital video player; a video player; a digital video disc (DVD) player; a portable digital video player; an automobile; a vehicle component; avionics systems; a drone; and a multicopter.
 22. A non-volatile (NV) memory (NVM) matrix circuit, comprising: a plurality of means for applying a plurality of input voltages representing an input vector; a plurality of means for applying a plurality of line voltages; a plurality of means for providing a plurality of output currents representing an output vector; a plurality of NVM storage string means each electrically coupled to a corresponding means for applying an input voltage among the plurality of means for applying the plurality of input voltages and a corresponding means for providing an output current among the plurality of means for providing the plurality of output currents, each of the plurality of NVM storage string means, comprising: a plurality of NV means for storing a memory state each having a resistance representing the stored memory state to form a data vector for a corresponding NVM storage string means among the plurality of NVM storage string means; each plurality of NV means for storing the memory state, comprising: a means for electrically coupling the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents; and a means for controlling coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents; and a plurality of access means for controlling the means for electrically coupling the corresponding means for applying the input voltage among the plurality of means for applying the plurality of input voltages to a corresponding NVM storage string means in the coupling of the resistance of the plurality of NV means for storing the memory state to the means for providing the output current among the plurality of means for providing the plurality of output currents.
 23. A method of performing matrix multiplication in a non-volatile (NV) memory (NVM) matrix circuit, comprising: applying a line voltage on at least one bit line among a plurality of bit lines coupled to a corresponding NVM storage string circuit among a plurality of NVM storage string circuits, to electrically couple the line voltage to the corresponding NVM storage string circuit coupled to a corresponding bit line among the plurality of bit lines, each NVM storage string circuit among the plurality of NVM storage string circuits comprising a plurality of NVM bit cell circuits each having a resistance representing a stored memory state in the NVM bit cell circuit to form a data vector for the corresponding NVM storage string circuit; applying a second line voltage on at least one source line among a plurality of source lines coupled to a corresponding NVM storage string circuit among the plurality of NVM storage string circuits, to electrically couple the second line voltage to the corresponding NVM storage string circuit coupled to a corresponding source line among the plurality of source lines; applying a plurality of input voltages representing an input vector on a plurality of word lines, each word line among the plurality of word lines coupled to a corresponding gate node of an NVM bit cell circuit in each of the plurality of NVM storage string circuits, to electrically couple the NVM bit cell circuit to the source line to couple the resistance of the NVM bit cell circuit to the source line; and applying an access voltage to a plurality of access transistors, each access transistor among the plurality of access transistors coupled to a corresponding bit line among the plurality of bit lines and a corresponding NVM storage string circuit among the plurality of NVM storage string circuits coupled to the source line corresponding to the bit line, to electrically couple the corresponding bit line to the corresponding NVM storage string circuit.
 24. The method of claim 23, further comprising generating a current flowing through a respective source line among the plurality of sources lines to a respective output node coupled to a respective NVM storage string circuit among the plurality of NVM storage string circuits based on a voltage applied to the bit line coupled to the respective NVM storage string circuit and the resistances applied by each of the plurality of NVM bit cell circuits of the respective NVM storage string circuit in response to a read activation voltage being applied to the gate nodes of each of the plurality of NVM bit cell circuits in the respective NVM storage string circuit.
 25. The method of claim 24, wherein an amplitude of the current flowing through the source line represents a dot product multiplication of the data vector of the NVM storage string circuit coupled to the source line, by the input vector.
 26. The method of claim 23, further comprising generating a plurality of currents flowing through each source line among the plurality of sources lines to a respective output node coupled to a respective NVM storage string circuits among the plurality of NVM storage string circuits based on a voltage applied to the bit line coupled to the respective NVM storage string circuit and the resistances applied by each of the plurality of NVM bit cell circuits of the respective NVM storage string circuit in response to a read activation voltage being applied to the gate nodes of each of the plurality of NVM bit cell circuits in the respective NVM storage string circuit.
 27. The method of claim 23, further comprising: applying a line voltage to a bit line among the plurality of bit lines coupled to a corresponding NVM storage string circuit among the plurality of NVM storage string circuits; applying a second line voltage to a source line among the plurality of source lines coupled to the corresponding NVM storage string circuit; and applying a write activation voltage to the gate node of the NVM bit cell circuit in the corresponding NVM storage string circuit to write a memory state based on the write activation voltage applied to the gate node of the NVM bit cell circuit.
 28. A non-volatile (NV) memory (NVM) matrix system, comprising: a first NVM matrix circuit, comprising: a plurality of first word lines configured to receive a first input vector represented by a first input voltage on each first word line among the plurality of first word lines; a plurality of first bit lines, each first bit line among the plurality of first bit lines configured to receive a corresponding first line voltage; a plurality of first source lines each coupled to a first output node among a plurality of first output nodes; a plurality of first NVM storage string circuits, each first NVM storage string circuit among the plurality of first NVM storage string circuits configured to be electrically coupled between a corresponding first bit line among the plurality of first bit lines and a corresponding first source line among the plurality of first source lines, each comprising a plurality of first NVM bit cell circuits; each first NVM bit cell circuit among the plurality of first NVM bit cell circuits having a resistance representing a stored memory state in the first NVM bit cell circuit to form a first data vector for the corresponding first NVM storage string circuit; and each first NVM bit cell circuit among the plurality of first NVM bit cell circuits in the first NVM storage string circuit, comprising: a first gate node coupled to a corresponding first word line among the plurality of first word lines; and each first NVM bit cell circuit configured to couple its resistance to the first source line in response to the first input voltage applied to the corresponding first word line coupled to the first gate node; and a second NVM matrix circuit, comprising: a plurality of second word lines each coupled to an output node among the plurality of first output nodes; a plurality of second bit lines, each second bit line among the plurality of second bit lines configured to receive a corresponding second line voltage; a plurality of second source lines each coupled to a second output node among a plurality of second output nodes; and a plurality of second NVM storage string circuits, each second NVM storage string circuit among the plurality of second NVM storage string circuits configured to be electrically coupled between a corresponding second bit line among the plurality of second bit lines and a corresponding second source line among the plurality of second source lines, each comprising a plurality of second NVM bit cell circuits; each second NVM bit cell circuit among the plurality of second NVM bit cell circuits having a resistance representing a stored memory state in the second NVM bit cell circuit to form a second data vector for the corresponding second NVM storage string circuit; and each second NVM bit cell circuit among the plurality of second NVM bit cell circuits in the second NVM storage string circuit, comprising: a second gate node coupled to a corresponding second word line among the plurality of second word lines; and each second NVM bit cell circuit configured to couple its resistance to the second source line in response to a second input voltage applied to the corresponding second word line coupled to the second gate node.
 29. The NVM matrix system of claim 28, wherein: the first NVM matrix circuit further comprises a plurality of first access transistors, each first access transistor among the plurality of first access transistors coupled to a corresponding first bit line among the plurality of first bit lines and a corresponding first NVM storage string circuit among the plurality of first NVM storage string circuits coupled to the first source line corresponding to the first bit line; each first access transistor among the plurality of first access transistors comprising a first access gate node coupled to a first access line; and each first access transistor among the plurality of first access transistors configured to electrically couple the corresponding first bit line to the corresponding first NVM storage string circuit in response to a first access voltage applied to the first access gate node; and the second NVM matrix circuit further comprises a plurality of second access transistors, each second access transistor among the plurality of second access transistors coupled to a corresponding second bit line among the plurality of second bit lines and a corresponding second NVM storage string circuit among the plurality of second NVM storage string circuits coupled to the second source line corresponding to the second bit line; each second access transistor among the plurality of second access transistors comprising a second access gate node coupled to a second access line; and each second access transistor among the plurality of second access transistors configured to electrically couple the corresponding second bit line to the corresponding second NVM storage string circuit in response to a second access voltage applied to the second access gate node.
 30. The NVM matrix system of claim 28, wherein: a first NVM storage string circuit among the plurality of first NVM storage string circuits is configured to generate a respective first current flowing through the first source line among the plurality of first source lines coupled to the first NVM storage string circuit to a respective first output node based on the first line voltage applied to the first bit line coupled to the first NVM storage string circuit and the resistances applied by each of the plurality of first NVM bit cell circuits of the first NVM storage string circuit in response to a first read activation voltage being applied to the first gate nodes of each of the plurality of first NVM bit cell circuits; and a second NVM storage string circuit among the plurality of second NVM storage string circuits is configured to generate a respective second current flowing through the second source line among the plurality of second source lines coupled to the second NVM storage string circuit to a respective second output node based on the second line voltage applied to the second bit line coupled to the second NVM storage string circuit and the resistances applied by each of the plurality of second NVM bit cell circuits of the second NVM storage string circuit in response to a second read activation voltage being applied to a first output node among the plurality of first output nodes of the first NVM matrix circuit coupled to the second gate nodes of each of the plurality of second NVM bit cell circuits. 